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ISSUED  BY  THE  MUTUAL  LIFE 
INSURANCE  COMPANY  OF  NEW  YORK 


Educational 
Leaflets 


Revised  December,  1 9 1 5 


copyright  191  5,  by 

The  Mutual  Life  Insurance  Company 

OF  New  York 


'% 


i. -'*'?'%-   "  *».,:7j'*'';i«\. 


INTRODUCTION 

'no  HE  Educational  Leaflets  of  The  Mutual  Life  Insur- 
-*-  ance  Company  of  New  York  were  first  issued 
serially,  in  the  year  1903,  and  afterwards  bound  in  a 
single  volume.  This  revision  of  the  work  is  published 
primarily  for  the  instruction  of  agents  of  the  Company 
just  entering  upon  their  career  as  solicitors.  It  follows 
that  the  matter  presented  is  at  first  of  an  elementary 
character,  and  the  language  employed  is  necessarily 
simple  and  free  from  technical  terms,  save  as  the  latter 
are  defined  with  the  progress  of  the  work.  The  aim  has 
been  to  adapt  the  language  used  to  the  comprehension 
of  the  beginner,  who  knows  absolutely  nothing  of  the 
subject;  but  the  decidedly  primary  character  of  the 
matter  treated  of  in  the  first  few  pages  will  gradually 
give  place  to  more  technical  discussions.  Every  new 
term  will  be  printed  in  italics  when  it  first  appears  and 
will  be  defined  at  once,  although  fuller  explanations  may 
come  later. 

The  work  is  designed  to  constitute  a  practical 
course  of  instruction  in  the  scientific  features  of  life 
insurance  to  the  extent,  at  least,  of  including  the  essen- 
tial elements  with  which  the  professional  solicitor  should 
be  familiar.  A  cross  index  will  be  provided  so  that  every 
definition  and  every  discussion  of  any  subject  may  be 
referred  to  readily. 

Life  insurance  is  now  generally  regarded  as  a 
profession,  and  as  that  view  gains  recognition,  a  pre- 
paratory   course   of    study   is    gradually   coming   to    be 

3 

336132 


deemed  important  if  not  essential.  Several  institutions 
have  been  recently  established  in  this  country  for  the 
purpose  of  teaching  insurance  by  correspondence,  and 
three  or  four  universities  have  already  included  in  their 
curricula  a  course  in  life  insurance,  while  others  provide 
frequent  lectures  on  the  subject.  It  is  probable,  there- 
fore, that  our  Managers  can  make  use  of  these  Educa- 
tional Leaflets  to  secure  many  good  agents  from  among 
those  just  entering  upon  the  work.  Such  persons  have 
here  the  opportunity  to  secure,  without  expense,  a 
thorough  course  of  instruction  in  the  principals  of  the 
business,  while  at  the  same  time  acquiring  a  practical 
knowledge  of  the  work  and  making  their  o^vn  living  by 
soliciting  insurance  under  the  direction  of  the  Manager. 

George  T.  Dexter, 

Second  Vice  President. 


CHAPTER  1 

Origin  of  Life  Insurance, 
Its  Character  and  Object 

PERVADING  all  nature  we  find  the  fundamental 
-*-  principle  of  life  insurance,  help  for  the  helpless. 
The  birds  of  the  air  provide  food  and  shelter  for  their 
nestlings.  The  beasts  of  the  field  minister  to  the  wants 
of  their  helpless  offspring.  Both  savage  and  civilized 
man  yield  to  the  promptings  of  this  universal  instinct 
in  caring  diligently  for  their  little  ones  and  for  their 
dependents. 

To  supply  the  immediate  needs  of  these  is  easy 
enough  for  the  young  and  the  strong,  but  the  true  man 
would  provide  also  for  their  future  necessities,  when,  by 
reason  of  ill  health  or  old  age,  he  is  no  longer  able  to 
care  for  them  through  his  personal  efforts.  This,  too, 
is  a  simple  problem  for  the  industrious  and  the  thrifty. 
One  has  only  to  lay  aside  regularly  and  to  invest  safely 
a  portion  of  his  income  to  have  in  a  few  years,  or  at 
most  in  old  age,  a  sufficient  dependence  for  his  family. 

But  suppose  death  were  to  intervene  before  this 
end  has  been  attained.  To  provide  for  this  contingency 
modern  Life  Insurance  has  been  devised.  In  its  sim- 
plest form,  a  number  of  persons  combine  to  create  a 
common  fund  to  be  drawn  upon  in  providing  for  the 
families  of  deceased  members  of  the  organization. 
Every  member  of  the  organization  has  a  voice  in  its 
management,  and  each  has  a  personal  interest  in  the 
accumulated  funds  of  the  society  in  proportion  to  the 
amount  he  has  contributed  thereto. 


Mutual  Companies 

Such  an  organization  is  appropriately  termed  a 
Mutual  Life  Insurance  Company.  The  contract  which 
is  made  by  the  company  with  the  member,  fixing  the 
amount  to  be  paid  in  the  event  of  his  death,  is  called 
a  Life  Insurance  Policy,  and  the  person  to  whom  the 
amount  is  payable  is  termed  the  Beneficiary.  The 
contract  or  policy  also  stipulates  the  amount  which  the 
member  is  to  contribute  to  the  common  fund,  and 
defines  his  rights  and  privileges  in  other  respects. 
The  person  holding  such  a  contract  is  termed  the 
Policy-holder.  The  contribution  to  be  made  by  him 
to  the  common  fund  as  stipulated  in  the  policy,  is 
termed  the  Premium,  and  this  is  usually  payable  yearly, 
or  in  half-yearly  or  quarterly  instalments. 

The  Mutual  Life  Insurance  Company  of  New 
York  is  precisely  such  an  organization  as  that  described 
above.  It  is  purely  mutual,  owned  and  controlled  by 
the  policy-holders,  and  is  directly  managed  by  a  board 
of  trustees  who  are  chosen  by  the  policy-holders.  Every 
member  of  The  Mutual  Life,  who  has  held  a  policy  for 
one  year  or  more,  is  entitled  to  one  vote  which  may  be 
forwarded  by  mail  or  cast  in  person  or  by  pro'xy.  At 
a  recent  election,  when  matters  of  special  importance 
were  under  consideration,  more  than  300,000  policy- 
holders expressed  their  choice  for  trustees  at  the  polls, 
nearly  ninety  per  cent,  of  whom  cast  their  votes  directly 
by  ballot,  in  most  cases  forwarded  by  mail. 

Stock  Companies 
There  is   another   class   of  companies  known   as 
Stock   Companies,  which  are  owned   and  controlled  by 


a  limited  number  of  individuals  termed  Stockholders, 
whose  respective  shares  or  interests  are  represented  and 
defined  by  a  written  instrument  termed  a  Certificate 
of  Stock.  These  shares  or  certificates  of  stock  may  be 
sold  or  transferred  at  the  will  of  the  holder,  and  the 
control  of  the  company  will  be  changed  accordingly.  The 
stockholders  of  such  an  organization  receive  a  portion 
or  all  of  the  savings  or  so-called  "profits"  of  the  business, 
and  the  officers  who  manage  its  affairs  are  chosen  from 
their  number.  When  the  policy-holders  of  such  a  com- 
pany share  with  the  stockholders  in  the  gains,  or  savings, 
the  organization  is  termed  a  Mixed  Company, 

In  The  Mutual  Life  Insurance  Company  of  New 
York  there  are  no  stockholders,  and  no  officer  or 
trustee  has  any  proprietary  interest  in  the  organization 
or  receives  any  perquisites  or  profits  by  reason  of  his 
position,  other  than  a  reasonable  compensation  for 
services  rendered.  His  interest  in  the  accumulated 
funds  of  the  Company  is  no  more  and  no  less  than  that 
of  any  other  policy-holder,  in  proportion  to  the  insur- 
ance carried  by  him.  In  the  control  of  the  Company  he 
has  but  a  single  vote,  the  same  as  any  other  policy- 
holder, irrespective  of  the  number  of  policies  or  the 
amount  of  insurance  carried  by  him. 

The  Mutual  Life  of  New  York  is  the  oldest  active 
company  in  America,  having  commenced  business  in 
February,  1843.  It  is  also  one  of  the  strongest  financial 
institutions  in  the  world.  As  before  stated,  its  assets  are 
the  property  of  the  policy-holders,  the  interest  of  each 
being  proportionate  to  the  amount  contributed  by  him 
thereto. 


Elementary  Principles 

Let  us  now  consider  some  of  the  underlying 
principles  of  scientific  life  insurance.  It  is  perhaps  not 
essential  to  the  solicitor's  success  that  he  be  proficient 
in  all  the  technicalities  of  the  science,  but  there  are 
some  things  which  he  must  know,  and  he  will  the  more 
readily  comprehend  and  acquire  these  if  he  under- 
stands at  least  the  elementary  principles  upon  which 
the  business  rests. 

To  illustrate  the  subject  we  shall  treat  first  of 
the  life  insurance  contract  in  its  commonest  form,  the 
Ordinary  Life  Policy.  In  the  case  of  this  contract  the 
premium  is  to  be  paid  every  year  during  the  life  of  the 
insured,  the  insurance  amount  being  payable  at  death. 
Before  entering  into  a  contract  of  this  kind  it  becomes 
necessary  to  fix  the  amount  of  the  premium,  which 
should  be  large  enough  to  enable  the  company  to 
meet  the  necessary  expense  of  conducting  the  business 
and  to  accumulate  a  fund  sufficient  to  pay  the  amount 
of  the  policy  when  the  same  matures  by  the  death  of 
the  insured. 

Making  the  Premium 

If  it  were  known  to  a  certainty  just  how  long 
the  policy-holder  would  live,  say,  for  example,  twenty 
years,  anyone  could  compute  the  amount  of  the 
necessary  premium.  Let  us  suppose,  for  illustration, 
that  the  face  of  the  policy  is  $1,000,  that  the  policy- 
holder will  live  just  twenty  years,  and,  to  simplify 
the  problem,  that  there  will  be  no  expenses  connected 

8 


with  the  business  and  no  interest  earned.  In  that  event, 
a  payment  of  $50.00  a  year  for  twenty  years  would 
amount  to  just  $1^000,  and  would  be  therefore  the  yearly 
premium  required. 

Let  us  assume,  however,  that  while  the  business 
is  still  conducted  without  expense,  the  premiums  are  all 
to  be  invested  at  interest  from  date  of  payment.  We 
do  not  know  to  a  certainty  what  rate  of  interest  can  be 
earned  during  the  whole  period,  and  we  shall  therefore 
assume  a  rate  that  we  can  safely  depend  upon,  say  three 
per  cent.  Any  schoolboy  will  solve  the  problem  now, 
and  tell  us  that  a  yearly  payment  of  $36.13  invested  at 
three  per  cent,  compound  interest  will  amount  to  $1,000 
in  twenty  years,  and  that  this  is  therefore  the  yearly 
premium  required. 

Observe  now,  that  if  it  were  certain  that  the 
policy-holder  would  live  just  twenty  years,  and  that  his 
premiums  would  earn  just  three  per  cent,  interest  and 
that  the  business  could  be  conducted  without  expense, 
the  necessary  premium  would  be  $36.13.  But  there 
will  be  expenses  and  there  are  certain  other  contin- 
gencies that  should  be  provided  for,  such,  for  example, 
as  a  loss  of  invested  funds,  or  a  failure  to  earn  the  full 
amount  of  three  per  cent,  interest. 

To  meet  these  expenses  and  contingencies  some- 
thing should  be  added  to  the  premium.  Let  us  estimate 
as  sufficient  for  this  purpose  the  sum  of  $7.00.  This  will 
make  our  gross  yearly  premium  $43.13,  the  original 
payment  ($36.13)  being  the  Net  Premium,  while  the 
amount  added  thereto  for  expenses,  etc.  ($7-00),  is 
termed  the  Loading. 


The  Net  Premium  is  the  amount  which  is  mathe- 
matically necessary  for  the  creation  of  a  fund  sufficient 
to  enable  the  Company  to  pay  the  policy  in  full  at 
maturity. 

The  Loading  is  the  amount  added  to  the  net 
premium  to  provide  for  expenses  and  contingencies. 

The  net  premium  and  loading  combined  make  up 
the  Gross  Premium,  or  the  total  sum  to  be  paid  yearly  by 

the  insured.  ' 

The  Mortality  Table 

If  it  were  known  to  a  certainty  how  long  any 
man  would  live,  the  business  of  life  insurance  would  be 
reduced  to  a  very  simple  basis — would  in  fact  become 
merely  a  commercial  transaction  of  saving  and  lending. 
Although  it  is  impossible  to  predict  in  advance  the  length 
of  any  individual  life,  as  in  the  illustration  given  above, 
there  is  a  law  governing  the  mortality  of  the  race 
by  which  we  may  calculate  the  average  lifetime  of  a 
large  number  of  persons  of  a  given  age.  We  cannot 
predict  in  what  year  the  particular  individual  will  die, 
but  we  may  determine  with  approximate  accuracy  how 
many  out  of  a  large  number  will  die  at  any  specified 
age.  By  means  of  this  law  it  becomes  possible  to  com- 
pute the  premium  necessary  to  be  charged  at  any  given 
age  with  almost  as  much  exactness  as  in  the  example 
given,  in  which  the  length  of  life  remaining  to  the 
individual  was  assumed  to  be  just  twenty  years. 

If  you  will  study  the  mortuary  records  of  any 
community  and  note  the  various  ages  at  which  the 
several  deaths  have  occurred,  you  will  find  the  yearly 
mortality  governed  by  a  law  which  is  practically 
invariable.      Let    us    suppose    for    example    that    your 

10 


observations  cover  a  period  of  time  sufficient  to  include 
the  history  of  100,000  lives.  Of  these  you  will  find  a 
certain  number  dying  at  age  thirty,  a  higher  death  rate  at 
age  forty,  and  so  on  at  the  various  ages,  the  extreme 
limit  of  life  reached  by  anyone  being  in  the  neighbor- 
hood of  one  hundred  years.  The  mortuary  records  of 
other  communities,  where  conditions  were  practically  the 
same,  would  give  approximately  the  same  results — the 
same  number  of  deaths  at  each  age  in  100,000  born. 
The  variHtion  would  not  be  great  and  the  larger  the 
number  of  lives  under  observation,  the  nearer  the  number 
of  deaths  at  the  several  ages  by  the  several  records  would 
approach  to  uniformity. 

In  this  manner  Mortality  Tables  have  been  con- 
structed which  show  how  many  in  any  large  number  of 
persons  born,  or  starting  at  a  certain  age,  will  live  to  age 
thirty,  how  many  to  age  forty,  how  many  to  any  other 
age,  and  likewise  the  number  that  will  die  at  each  age, 
with  the  average  lifetime  remaining  to  those  still  alive. 

The  American  Experience  Table  of  Mortality  was 
constructed  about  the  year  1861  by  Sheppard  Homans, 
the  then  Actuary  of  The  Mutual  Life  Insurance  Com- 
pany of  New  York,  and  was  based  mainly  upon  the 
history  of  lives  insured  in  that  company.  The  table  be- 
gins with  100,000  persons  at  age  ten  and  fixes  the  Limit 
of  Life  at  ninety-six  years — the  attained  age  at  which 
the  last  three  of  the  original  100,000  are  assumed  to 
die.  The  premium  rates  of  practically  all  American 
companies  are  based  upon  this  table.  Fuller  information 
regarding  this  and  other  mortality  tables  will  be  given 
in  a  later  article. 

In  the  next  chapter  we  shall  show  how  the  neces- 
sary premium  in  practical  life  insurance  is  determined 
with  the  aid  of  the  mortality  table. 


CHAPTER  II 

The  Computation  of  the  Premium 

\\T  E  propose  now  to  explain  the  computation  of  the 
life  insurance  premium.  This  is  information  which, 
in  one  sense,  is  not  essential  to  the  success  of  the  solicitor, 
since  he  finds  his  premiums  ready-made  in  his  rate  book; 
but  a  knowledge  of  the  principle  involved  in  the  com- 
putation is  essential  to  a  perfect  comprehension  of  other 
matters  which  he  must  know. 

We  present  for  reference  on  page  1 3  the  American 
Experience  Table  of  Mortality  defined  in  the  previous 
chapter    (page  11). 

As  heretofore  explained  the  table  begins  with 
100,000  lives,  starting  with  the  age  of  ten  years.  Of 
these,  81,822  will  still  be  living  at  the  age  of  thirty-five 
of  whom  732  will  die  during  the  year.  This  will  leave 
81,090  still  living  at  the  beginning  of  the  next  year  at 
age  thirty-six,  while  737  of  this  number  will  die  in  the 
ensuing  twelve  months.  At  age  fifty-six  there  will  be 
living  63,364  of  the  original  number  and  of  these,  1,260 
will  die  during  the  year.  In  the  same  way  the  table 
shows  how  many  of  the  original  100,000  are  living  at 
each  age  from  ten  years  on,  and  how  many  will  die  in 
each  year  thereafter  until  the  last  three,  who  have  lived 
to  attain  the  age  of  ninety-five,  are  assumed  to  pass  away 
during  or  at  the  end  of  that  year,  none  living  beyond  the 
attained  age  of  ninety-six. 

A  Hypothetical  Company 
Let  us  suppose,  now,  that  we  have  organized  a  life 
insurance   company  composed   of   63,364   persons,   each 

12 


American  Experience  Table  of  Mortality 


Hamber 

Deathg 

Deatli- 

Expecta- 

Naml)er 

Deatlis 

Deatli- 

Expecta. 

Age 

Each 

rate 

tion  of 

Age 

Living 

Each 

rate 

tion  of 

Living 

Tear 

Per  1,000 

Life 

Year 

Per  1,000 

Life 

10 

100,000 

749 

7.49 

48.72 

53 

66,797 

1,091 

16.33 

18.79 

11 

99,251 

746 

7.52 

48.08 

54 

65,706 

1,143 

17.40 

18.09 

la 

98,505 

743 

7.54 

47.45 

55 

64,563 

1,199 

18.57 

17.40 

13 

97,762 

740 

7.57 

46.80 

56 

63,364 

1,260 

19.88 

16.72 

14 

97,022 

737 

7.60 

46.16 

57 

62,104 

1,325 

21.33 

16.05 

IS 

96,285 

735 

7.63 

45.50 

58 

60,779 

1,894 

22.94 

15.39 

16 

95,550 

732 

7.66 

44.85 

59 

59,385 

1,468 

24.72 

14.74 

17 

94,818 

729 

7.69 

44.19 

60 

57,917 

1,546 

26.69 

14.10 

18 

94,089 

727 

7.73 

43.53 

61 

56,871 

1,628 

28.88 

13.47 

19 

93,362 

725 

7.76 

42.87 

62 

54,748 

1,718 

81.29 

12.&> 

20 

92,637 

723 

7.80 

42.20 

63 

58,030 

1,800 

33.94 

12.26 

31 

91,914 

722 

7.85 

41.53 

64 

51,280 

1,889 

86.87 

11.67 

22 

91,192 

721 

7.91 

40.85 

65 

49,341 

1,980 

40.18 

11.10 

23 

90,471 

720 

7.96 

40.17 

66 

47,361 

2,070 

43.71 

10.54 

24 

89,751 

719 

8.01 

39.49 

67 

45,291 

2,158 

47.65 

10.00 

25 

89,032 

718 

8.06 

38.81 

68 

43,133 

2,243 

52.00 

9.47 

26 

88,314 

718 

8.13 

38.12 

69 

40,890 

2,321 

56.76 

8.97 

27 

87,596 

718 

8.20 

37.43 

70 

38,569 

2,891 

61.99 

8.48 

28 

86,878 

718 

8.26 

36.73 

71 

36,178 

2,448 

67.66 

8.00 

29 

86,160 

719 

8.34 

36.03 

72 

33,730 

2,487 

73.73 

7.55 

30 

85,441 

720 

8.43 

35.33 

73 

31,243 

2,505 

80.18 

7.11 

31 

84,721 

721 

8.51 

34.68 

74 

28,738 

2,501 

87.03 

6.68 

32 

84,000 

728 

8.61 

83.92 

75 

20,287 

2,476 

94.37 

6.27 

33 

83,277 

726 

8.72 

33.21 

76 

23,761 

2,431 

102.31 

6.88 

34 

82,551 

729 

8.83 

32.50 

77 

21,330 

2,869 

111.06 

6.49 

35 

81,822 

732 

8.95 

31.78 

78 

18,961 

2,291 

120.83 

5.11 

36 

81,090 

737 

9.09 

31.07 

79 

16,670 

2,196 

131.73 

4.74 

37 

80,353 

742 

9.23 

30.35 

80 

14,474 

2,091 

144.47 

4.89 

38 

79,611 

749 

9.41 

29.62 

81 

12,383 

1,964 

158.60 

4.05 

39 

78,862 

756 

9.59 

28.90 

82 

10,419 

1,816 

174.30 

8.71 

40 

78,106 

765 

9.79 

28.18 

83 

8,603 

1,648 

191.56 

3.39 

41 

77,341 

774 

10.01 

27.45 

84 

6,955 

1,470 

211.36 

3.08 

42 

76,567 

785 

10.25 

26.72 

85 

5,485 

1,292 

235.55 

2.77 

43 

75,782 

797 

10.52 

26.00 

86 

4,193 

1,114 

265.68 

2.47 

44 

74,985 

812 

10.83 

25.27 

87 

3,079 

938 

303.02 

2.18 

45 

74,173 

828 

11.16 

24.54 

88 

2.146 

744 

348.69 

1.91 

46 

73,345 

848 

11.50 

23.81 

89 

1,402 

555 

895.86 

1.66 

47 

72,497 

870 

12.00 

23.08 

90 

847 

885 

454.54 

1.42 

48 

71,627 

896 

12.51 

22.36 

91 

462 

246 

582.47 

1.19 

49 

70,731 

927 

13.11 

21.63 

92 

216 

137 

634.26 

.98 

50 

69,804 

962 

13.78 

20.91 

93 

79 

58 

734.18 

.80 

51 

68,842 

1,001 

14.54 

20.20 

94 

21 

18 

857.14 

.64 

52 

67,841 

1,044 

15.39 

19.49 

95 

3 

3 

1000.00 

.50 

fifty-six  years  of  age,  and  each  insured  for  $1,000  payable 
at  death.  We  take  the  figures  63,364  as  our  total  mem- 
bership merely  for  convenience  sake,  that  being  the 
number  of  persons  still  living  at  age  fifty-six  as  given  in 


18 


the  mortality  table.  If  we  can  show  what  premium  it 
would  be  necessary  to  collect  at  age  fifty-six,  we  can  by 
the  same  process  determine  the  required  premium  for  any 
other  age.  It  is  also  for  convenience  sake — to  make  the 
problem  as  simple  as  possible — ^that  we  assume  that  each 
member  of  our  hypothetical  company  will  maintain  his 
membership  during  his  entire  lifetime,  and  that  no  new 
members  will  be  added  after  the  date  of  organization. 
Withdrawals  and  additions  have  no  effect  upon  the  amount 
of  premium  which  it  is  necessary  to  collect  to  enable  the 
company  to  fulfill  its  contracts,  all  of  which  will  be  more 
fully  explained  hereafter.  In  the  same  way,  although 
members  may  die  at  any  time  during  the  year,  and  the 
practice  is  to  pay  losses  as  soon  as  possible  after  death, 
yet,  theoretically,  these  losses  are  payable  at  the  end  of 
the  year,  and  our  computations  are  made  on  that  basis. 
The  practice  of  paying  claims  before  the  end  of  the  year 
merely  involves  the  loss  of  a  little  interest  which  the 
companies  more  than  make  up  from  other  sources. 

We  have  then  63,364  persons  insured,  each  of 
whom  is  to  receive  at  death  $1,000.  This  will  make 
a  total  ultimately  to  be  paid  of  $63,364,000.  This 
enormous  sum  is  to  come  entirely  from  the  premiums 
that  are  to  be  paid  by  the  original  63,364  members  and 
the  interest  which  those  premiums  will  earn.  The  prob- 
lem now  is  to  determine  how  large  a  premium  each  mem- 
ber must  pay  in  order  to  create  a  fund  which,  with  the 
interest  to  be  earned,  will  be  sufficient  for  this  purpose. 

The  First  Step 

If  we  could  start  out  on  the  day  of  organization 
with  this  fund  complete — money  enough  in  hand  to  pay 
every  one  of  these  policies  in  full  as  it  matures  by  the 

14 


death  of  the  member,  the  business  would  be  greatly 
simplified.  We  should  then  have  no  occasion  to  worry 
regarding  future  withdrawals  and  collections,  nor  con- 
cerning the  ability  of  the  company  to  pay  the  last  man 
in  full,  even  without  the  influx  of  "new  blood" — ^the 
addition  of  new  members.  This  is  in  fact  the  essential 
principle  involved  in  so-called  "old  line"  life  insurance 
— the  collection  of  a  premium  large  enough  to  maintain 
a  fund  sufficient  for  the  ultimate  payment  of  all  existing 
policies  without  the  necessity  of  adding  new  members. 
The  first  step  to  be  taken  then  is  to  ascertain  how  large 
a  total  fund  we  ought  to  have  on  hand  at  once  for  the 
accomplishment  of  this  end. 

Turn  now  to  the  figures  of  the  mortality  table 
given  above.  We  have  63,364  members  all  of  whom, 
according  to  the  table,  will  die  within  the  next  forty 
years.  We  do  not  know  when  any  particular  one  will 
die,  nor  how  long  any  individual  member  will  live.  The 
amount  that  each  member  should  pay,  therefore,  cannot 
be  determined  by  means  of  a  computation  based  upon  a 
single  life,  as  in  the  example  heretofore  given  on  page  8. 
But  if  we  do  not  know  how  long  any  one  individual  will 
live,  the  mortality  table  tells  us  how  long  certain  groups 
of  members  will  live.  For  example,  we  see  by  the  table 
that,  of  the  members  of  our  company  living  at  age  fifty- 
six,  1,260  will  live  not  more  than  one  year;  that  1,980 
will  die  in  the  tenth  year;  1,292  in  the  thirtieth  year, 
etc. ;  and  that  the  last  three  will  live  not  to  exceed  forty 
years,  to  age  ninety-six.  We  must  base  our  computations 
then,  upon  the  aggregate  number  of  lives — the  length  of 
time  the  members  will  live  as  a  body,  as  shown  in  the 
case  of  these  several  groups. 

15 


Referring  to  the  table^  for  example,  we  see  that 
1,980  members  will  die  during  or  at  the  end  of  the  tenth 
year,  at  the  attained  age  of  sixty-six.  We  know  there- 
fore that  we  shall  need  $1,980,000  at  the  end  of  the 
tenth  year  in  order  to  pay  $1,000  for  each  death.  We 
do  not  need  that  amount  on  hand  to-day,  for  our  funds 
will  earn  some  interest  during  the  next  ten  years.  We 
require  therefore,  at  this  time,  only  a  sum  sufficient  to 
amount  to  $1,980,000  in  ten  years,  at  such  rate  of 
interest  as  can  be  earned. 

The  Interest  Rate  in  Life  Insurance 

Here  again  we  do  not  know  what  amount  of 
interest  will  be  earned.  A  rate  of  five  or  six  per  cent,  or 
a  little  more,  may  be  had  in  some  cases,  but  as  a  rule  the 
rate  will  be  less  and  we  shall  also  have  a  small  amount  of 
idle  funds  on  hand  at  times.  Above  all,  a  safe  investment 
is  to  be  preferred  to  large  earnings,  and  it  is  a  rule  of 
finance  that,  the  higher  the  ratio  of  profit  the  poorer  the 
security.  It  follows  that  in  our  haste  to  gain  large  earn- 
ings, the  principal  itself  might  be  lost,  thus  defeating  the 
purpose  of  our  organization.  That  must  not  be.  In  life  in- 
surance, first  of  all,  the  funds  must  be  safe.  It  would  be 
no  misfortune  to  have  an  accumulation  larger  than  needed, 
but  an  insufficient  fund  would  mean  that  widows  and 
orphans  must  suffer.  We  must  therefore  assume  a  rate 
of  interest  such  as  the  safest  possible  class  of  securities 
may  be  depended  upon  to  earn,  not  now  merely  but  for 
many  years  to  come.  On  that  basis  The  Mutual  Life 
Insurance  Company  of  New  York  assumes  that  its  invested 
funds  will  earn  on  the  average  not  less  than  three  per 

16 


cent.  That  they  will  earn  a  higher  rate  than  that  for 
many  years  may  be  conceded  as  certain.  If  it  were  not 
certain^  less  might  be  earned,  for  the  exact  rate  cannot 
be  determined  in  advance. 

The  present  worth  of  $1,980,000  due  in  ten  years 
is  $1,473,305.94,  that  being  the  sum  which  at  three  per 
cent,  interest  will  amount  to  $1,980,000  in  ten  years.  If 
we  have  that  amount  on  hand  to-day  and  can  safely  in- 
vest it  at  three  per  cent,  interest,  it  is  mathematically 
certain  that  we  shall  be  able  to  pay  the  death  claims  of 
the  tenth  year. 

Turning  again  to  the  mortality  table,  we  see  that 
in  the  twenty-fifth  year,  at  age  eighty,  there  will  be 
2,091  deaths  calling  for  the  payment  at  the  end  of  that 
year  of  $2,091,000.  The  present  worth  of  that  sum  at 
three  per  cent,  is  $998,673.25.  If  then  we  have  that 
much  on  hand  to-day  for  use  in  the  twenty-fifth  year 
and  it  can  be  safely  invested  at  three  per  cent,  interest, 
it  is  mathematically  certain  that  we  shall  be  able  again 
to  pay  the  death  claims  of  that  year. 

Or  take  the  1,260  deaths  of  the  first  year.  These 
claims,  payable  at  the  end  of  the  year,  call  for  the  sum 
of  $1,260,000  and  the  present  worth  of  that  amount  due 
in  one  year  is  $1,223,300.98. 

Is  it  not  clear  that  we  can  in  like  manner  deter- 
mine from  the  mortality  table  what  our  losses  will  be  for 
each  year,  even  to  the  last  or  fortieth  year,  when  the 
death  claims  will  amount  to  $3,000?  And  can  we  not 
thus  find  the  present  worth  of  the  amounts  which  will  be 
needed  in  each  and  every  year  to  pay  all  the  claims  of 
such  years  until  the  last  three  members  pass  away  in  the 

17 


fortieth  year  of  their  membership,  at  the  attained  age 
of  ninety-six?  Nine  hundred  and  nineteen  dollars  and 
sixty-seven  cents  on  hand  to-day  will  amount  in  forty 
years,  at  three  per  cent,  interest,  to  $3,000,  or  sufficient 
to  pay  in  full  the  policies  of  the  last  three  members  of 
our  company. 

The  Total  Insurance  Fund 
In    the    following   table,   we    have    arranged    in 
columns  the  death  claims  of  the  first,  tenth,  twenty-fifth 
and  fortieth  years  as  given  above: 

Age  Attained 

Begin-  ^  Age  Death  Present  Worth 

ning  of  *  ^'^'-  End  of  Claims  of  Claims 

Year  Year 

56  First  year  57     $1,260,000     $1,223,300.98 

*  *  *  *  * 

65  Tenth  year  66       1,980,000       1,473,305.94 

*  *  ^  *  * 

80  Twenty-fifth  year  81       2,091,000  998,673.25 

¥f  ^^  *  *  * 

95  Fortieth  year           96  3,000  919.67 

Totals $63,364,000  $39,360,583.39 

The  stars  take  the  place  of  the  other  years  as 
given  in  the  complete  mortality  table  for  the  several  ages 
from  fifty-six  on,  the  figures  for  which  may  be  deter- 
mined in  the  same  manner. 

You  may  work  it  out  for  yourself.  Note  the 
number  of  deaths  in  each  year  according  to  the  mortality 
table  until  the  last  three  members  die.  Find  the  present 
worth  of  the  amount  required  in  each  year  for  payment 

18 


of  claims,  and  place  in  the  column  headed  present  worth. 
Find  the  total  of  these  present  worths,  and  you  will  get 
the  sum  of  $39,360,583.39. 

With  this  amount  on  hand  to-day,  on  the  assump- 
tion that  the  same  will  earn  three  per  cent,  interest, 
we  shall  have  funds  sufficient  for  the  payment  of  every 
death  claim  that  can  possibly  occur,  according  to  the 
mortality  table,  in  any  year  until  the  last  three  members 
die,  in  the  ninety-sixth  year  of  their  age.  That  sum 
divided  by  63,364,  the  number  originally  insured  in  our 
hypothetical  company,  gives  $621.18...  In  other  words, 
if  each  member  of  our  Company  will  pay  in  cash  the  sum 
of  $621.18...,  we  shall  have  at  date  of  organization  a 
total  of  $39,360,583.39,  or  sufficient  to  pay  every  existing 
policy  in  full  as  the  several  deaths  occur.  This  $621.18 
is  termed  the  Net  Single  Premium,  and  is  the  net  amount, 
without  provision  for  expenses,  which  a  man  at  age 
fifty-six  should  pay  for  a  full  paid  policy  of  $1,000. 

The  net  single  premium  having  been  deposited, 
no  further  payments  would  ever  be  required,  but  most 
men  would  find  it  inconvenient  to  pay  for  their  life  insur- 
ance in  a  single  sum.  By  means,  however,  of  an  equally 
simple  mathematical  process  we  may  apportion  that  net 
single  premium  into  equivalent  yearly  payments  to  be 
made  by  the  insured  during  life.  Before  entering  into 
an  explanation  of  that  process,  it  becomes  necessary  to 
explain  the  meaning  of  several  new  terms  which  will  be 
taken  up  in  the  next  chapter. 


19 


chapter  iii 
The  Life  Annuity 

IT  is  our  purpose  to  show  now  how  the  net  single 
premium  may  be  apportioned  into  small  yearly  pay- 
ments, to  be  made  during  life,  which  shall  be  the  exact 
mathematical  equivalent  of  the  former.  To  understand 
the  process,  one  must  know  something  of  annuities. 

An  Annuity  is  a  specific  sum  of  money  to  be  paid 
yearly  to  some  designated  person.  The  one  to  whom 
the  money  is  to  be  paid  is  termed  the  Annuitant,  If 
the  payment  is  to  be  made  every  year  until  the  annuitant 
dies,  it  is  termed  a  Life  Annuity.  For  example,  a  life 
insurance  company  or  other  financial  institution,  in  con- 
sideration of  the  payment  to  it  of  a  specified  amount, 
say  $1,000,  will  enter  into  a  contract  to  pay  a  desig- 
nated annuitant  a  stated  sum,  say  $100,  on  a  specified 
day  in  every  year  so  long  as  the  annuitant  continues  to 
live.  The  latter  may  live  to  draw  his  annuity  for  many 
years,  until  he  has  received  in  the  aggregate  several 
times  the  original  amount  paid  by  him,  or  he  may  die 
after  having  collected  but  a  single  payment,  or  even 
earlier.  In  either  case  the  contract  expires  and  the 
annuity  terminates  with  the  death  of  the  annuitant. 

The  amount  of  yearly  income  or  annuity  which 
can  be  purchased  with  $1,000  will  depend  of  course 
upon  the  age  of  the  annuitant.  That  sum  will  buy  a 
larger  income  for  a  man  of  seventy  than  for  one  of  fifty- 
six,  for  the  reason  that  the  former  has,  on  the  average, 
a  much  shorter  time  yet  to  live.     The  net  cost  of  an 

20 


annuity,  that  is,  the  net  amount  to  be  paid  therefor  in 
one  sum,  and  which  is  termed  the  Value  of  the  Annuity, 
is  not  a  matter  of  estimate  but,  like  the  life  insurance 
premium,  is  determined  by  mathematical  computation, 
based  upon  the  mortality  table.  The  process  is  quite  as 
simple  as  the  computation  of  the  single  premium,  and 
exactly  similar. 


Computing  the  Value  of  the  Annuity 

Let  us  undertake,  for  example,  to  determine  the 
net  amount  which  a  company  should  charge  in  a  single 
sum  for  a  life  annuity  of  $1.00  to  be  paid  to  every  one 
of  63,364  persons,  all  of  the  age  of  fifty-six  years,  the 
first  payment  to  be  made  immediately  on  the  execution 
of  the  contract.  The  figures  named  will  be  recognized 
as  the  number  of  persons  still  living  at  age  fifty-six 
out  of  100,000  starting  at  age  ten,  as  given  in  the 
American  Experience  Table  of  Mortality,  page  13,  and 
already  adopted  in  our  hypothetical  life  insurance 
company. 

As  each  person  is  to  receive  $1.00  immediately, 
it  is  obvious  that  the  company  will  require  a  sum  in  hand 
of  $63,364.00  in  order  to  pay  the  annuities  due  at  the 
beginning  of  the  first  year,  on  the  execution  of  the 
contract. 

It  will  also  be  seen  by  the  table  that  1,260  annui- 
tants will  die  during  the  first  year  after  having  received 
but  one  payment.  Nothing  more  is  to  be  paid  on  their 
account.     This  leaves  62,104  persons  still  living  on  the 

21 


first  day  of  the  second  year,  each  of  whom  is  to  receive 
a  payment  of  $1.00  on  that  day.  The  company  will 
require  therefore  to  have  on  hand  at  the  beginning  of 
the  second  year  a  total  of  $62,104.00  to  pay  the  annui- 
ties then  due.  The  present  worth  of  that  sum  at  three 
per  cent,  is  $60,295.15,  which  represents,  therefore, 
the  amount  that  it  should  have  in  its  possession  to-day 
to  enable  it  to  pay  the  annuities  due  one  year  hence. 

Turning  to  the  table  again  we  find  49,341  per- 
sons still  living  at  the  beginning  of  the  tenth  year  at 
age  sixty-five  and  each  of  these  is  to  receive  $1.00,  re- 
quiring a  total  payment  on  that  day  of  $49,341.00.  The 
present  worth  of  that  sum  at  three  per  cent,  interest  due 
in  nine  years  is  $37,815.77,  which  represents  the  amount 
the  company  must  have  on  hand  to-day  to  enable  it  to 
pay  the  annuities  due  at  the  beginning  of  the  tenth  year. 

There  will  be  three  persons  living  on  the  first 
day  of  the  fortieth  year  at  age  ninety-five,  requiring 
the  payment  on  that  day  of  $3.00,  the  present  worth  of 
which  sum  payable  thirty-nine  years  hence  is  $0,947,  or 
ninety-five  cents. 

It  is  not  necessary  to  illustrate  further  the  pro- 
cess by  which  we  determine  the  present  worth  of  the 
several  amounts  to  be  paid  out  in  annuities  to  those 
living  at  the  beginning  of  each  year  until  the  last  three 
of  the  original  63,364  pass  away  in  the  fortieth  year. 
As  in  the  computation  of  the  single  premium,  we  have 
arranged  in  columns  in  the  following  table  the  several 
amounts  to  be  paid  out  in  annuities  at  the  beginning  of 
the  first,  the  second,  the  tenth  and  the  fortieth  years  and 
the  present  worth  of  those  sums  as  given  above. 


Age 
Begin- 
ning  of 
Year 

Year 

Number 
Uving 

A  nnuities 
to  be  paid 

Present  Worth 
of  Annuities. 

56 

First  year 

63,364 

$63,364 

$63,364.00 

57 

Second  year 

62,104 

62,104 

60,295.15 

65 
* 

Tenth  year 

49,341 

49,341 

37,815.77 
* 

95 

Fortieth  year 
Totals. 

3 

3 

0.95 

$1,091,123 

$824,117.31 

The  stars  represent  the  figures  for  the  ages 
omitted.  If  these  omissions  be  correctly  supplied, 
the  total  of  all  the  present  worths  will  be  as  given, 
$824,117.31.  But  $824,117.31  divided  by  63,364  gives 
just  $13.006...,  or  thirteen  dollars  and  one  cent.  If, 
therefore,  each  one  of  our  original  63,364  persons  at  age 
fifty-six  will  contribute  the  sum  of  $13. 006... toward  the 
creation  of  an  annuity  fund,  we  shall  have  a  total  of 
$824,117.31,  or  just  enough  to  pay  each  man  an  annuity 
of  one  dollar  at  the  beginning  of  each  year  so  long  as  he 
lives,  provided  that  the  deaths  occur  as  indicated  by  the 
mortality  table,  and  that  our  funds  earn  three  per  cent, 
interest. 

To  Find  the  Net  Annual   Premium 

The  value,  or  cost,  of  a  life  annuity  of  $1.00  at 
age  fifty-six  by  the  American  Experience  Table  and 
three  per  cent,  interest,  is  thus  found  to  be  $13,006. 
In  other  words,  $13,006  paid  down  in  one  sum  is  the 
exact   mathematical   equivalent   at  age   fifty-six   of  the 

S8 


payment  of  $1.00  at  the  beginning  of  each  year  during 
life.  We  have  seen  that  the  net  single  premium  for 
$1,000  life  insurance  at  age  fifty-six  is  $621.18.  If 
$13,006  is  the  mathematical  equivalent  of  $1.00  to  be 
paid  annually  during  life,  $621.18  must  be  the  mathe- 
matical equivalent  of  as  many  dollars  to  be  paid  yearly 
during  life,  as  $13,006  is  contained  times  in  $621.18. 
Performing  the  division  we  get  $47.76.  In  other  words, 
$47.76  paid  at  the  beginning  of  each  year  during  life  is 
the  exact  equivalent  of  the  net  single  premium  of 
$621.18,  and  is  therefore  the  net  annual  premium  of  an 
ordinary  life  policy  of  $1,000  at  age  fifty-six,  accord- 
ing to  the  American  Experience  Table  and  three  per 
cent,  interest. 

General  Observations 

We  have  seen  that  at  age  fifty-six  the  sum  of 
$13,006  will  purchase  a  life  annuity  of  $1.00;  in  other 
words,  $13,006  paid  in  one  sum  is  the  mathematical 
equivalent  of  $1.00  to  be  paid  at  the  beginning  of  every 
year  during  life. 

We  have  also  seen  that  $621.18  paid  in  one  sum 
is  the  mathematical  equivalent  of  $47.76  paid  yearly 
during  life. 

These  equivalents  may  be  expressed  in  the  fol- 
lowing proportion: 

$13,006     :    $1.00     ::    $621.18     :    $47.76 

That  is,  the  value  of  a  life  annuity  of  $1.00,  is 
to  $1.00,  as  the  net  single  premium  at  the  same  age  is  to 
the  equivalent  net  annual  premium. 


Observe  that  the  value  of  a  life  annuity  of  $47.76 
at  age  56  would  be  $621.18;  that  is  to  say  the  net  single 
premium  of  an  ordinary  life  policy  will  purchase  a  life 
annuity  equal  in  amount  to  the  net  annual  premium  of 
the  same  policy. 

In  all  these  observations  we  speak  of  net  pre- 
miums only,  the  matter  of  loading  for  expenses  remain- 
ing to  be  adjusted. 

Sufficiency  of  the  Premium 

If  you  have  read  the  preceding  pages  with  care 
you  have  now  some  comprehension  of  the  scientific  basis 
of  life  insurance.  You  now  know  for  yourself  that  it  is 
possible  to  determine  in  advance  the  cost  of  insuring  a 
given  number  of  lives.  You  know  for  yourself  that  the 
premium,  mathematically  computed  in  the  manner  set 
forth,  is  sufficient  for  the  payment  of  all  claims  that  can 
ever  occur  until  the  last  policy  has  matured  by  the  death 
of  the  insured. 

There  can  be  no  uncertainty  as  to  the  adequacy 
of  the  premium  so  computed.  There  may,  indeed,  be 
uncertainty  as  to  the  rate  of  interest  to  be  received,  but 
only  in  respect  of  what  the  excess  may  be.  We  may 
easily  earn  more  than  the  rate  assumed,  but  that  rate  is 
so  low  that  it  is  morally  certain  that,  through  a  series  of 
years,  we  shall  not  average  less.  It  is  therefore  certain 
that,  while  the  premium  may  be  larger  than  necessary 
by  reason  of  the  increased  interest  earnings,  it  cannot  be 
smaller  than  is  requisite.  The  mortality,  likewise,  may 
prove  to  be  less  than  indicated  by  the  table,  but  the 
universal    experience    of    well-managed    companies    has 

86 


demonstrated  that,  through  a  series  of  years,  it  will  not 
average  more  than  the  tabular  rate.  This  again  means 
that,  by  reason  of  a  low  mortality,  our  premium  may 
prove  larger  than  necessary,  but  it  will  not  be  smaller 
than  required. 

It  is  better  that  the  premium  should  be  too  large 
than  too  small.  To  have  on  hand  more  funds  than  may, 
perchance,  be  needed  for  the  payment  of  death  claims  is 
not  a  serious  misfortune;  since  the  excess  can  be  returned 
to  the  policy-holders  subsequently.  To  have  less  than 
sufficient  for  the  payment  of  claims  would  mean  insol- 
vency and  dissolution. 

Effect  of  Withdrawals 

In  our  hypothetical  company  it  was  assumed  that 
all  members  would  continue  to  pay  their  premiums  until 
death.  In  practice  it  is  well  known  that  many  with- 
draw after  having  made  one  or  more  payments.  The 
member  who  drops  out,  thereby  forfeiting  the  payments 
he  has  already  made,  is  said  to  Lapse,  The  question 
arises,  what  allowance  should  be  made  in  the  computa- 
tion of  the  premium  for  the  gains  that  may  accrue  from 
lapses?  We  shall  answer  this  question  only  briefly  and 
partially  now,  but  more  fully  in  a  later  chapter. 

That  there  will  be  lapses  is  certain,  but  it  does 
not  follow  that  there  will  be  a  real  gain  from  that  source. 
Experience  has  shown  that  it  is  the  sound  life  as  a  rule 
that  withdraws.  After  a  company  has  been  in  existence 
for  some  years  many  of  the  members  are  in  impaired 
health.     These  are  not  likely  to  lapse.     The  man  who  is 

26 


about  to  die  will  cling  to  his  insurance.  The  man  who 
is  in  robust  health  is  the  one  to  withdraw.  It  is  con- 
ceivable that  lapses  might  multiply  until  presently  we 
should  have  merely  a  company  of  invalids  with  a  mor- 
tality in  excess  of  any  known  table.  In  other  words,  the 
apparent  gain  from  lapses  is  apt  to  be  offset  by  an 
increased  mortality. 

It  is  impossible  to  determine  in  advance  what  the 
lapse  rate  of  any  company  will  be,  or  what  will  be  the 
relative  proportions  of  invalids  and  sound  lives  among 
the  withdrawing  members.  It  is  impossible,  therefore, 
to  determine  beforehand  what  allowance,  if  any,  should 
be  made  on  account  of  the  possible  profits  accruing  from 
that  source.  Accordingly,  it  is  assumed  in  the  compu- 
tation of  the  premium  that  there  will  be  no  lapses  and 
hence  no  gains  therefrom.  If,  as  a  matter  of  subse- 
quent experience,  there  prove  to  be  such  gains,  then, 
as  in  the  case  of  excess  interest  and  savings  in  mortality, 
the  surplus  thus  accruing  will  be  apportioned  equitably 
among  the  members,  after  it  is  known  that  there  has 
been  a  gain  from  that  source. 

Notwithstanding  the  fact  that  the  impaired  risk 
is  not  apt  to  lapse  his  policy,  there  are  indications  that 
the  mortality  among  withdrawals  in  after-life  is  as  great 
as  among  the  body  of  persistent  members,  for  the  reason 
that  many  of  those  that  withdraw  under  normal  condi- 
tions are  of  the  shiftless,  vacillating  class  who  are  less 
likely  to  live  to  old  age  than  the  thrifty,  determined  class. 
However  this  may  be,  nothing  is  more  clearly  demon- 
strated than  that  when  lapses  are  excessive,  as   when 

27 


the  policy-holders  have  lost  confidence  in  the  company  or 
its  management,  the  sound  lives  who  can  secure  insur- 
ance elsewhere  withdraw  in  much  larger  proportion  than 
under  ordinary  conditions.  This  is  clearly  shown  by  the 
excessive  mortality  in  companies  which  have  suffered 
from  heavy  withdrawals  due  to  lack  of  confidence  in  the 
management  or  in  the  plan  of  insurance,  as  shown  by 
the  abnormal  mortality  in  decadent  assessment  companies. 

Effect  of  New  Members 

Another  question  naturally  arising  is,  would  not 
the  addition  of  new  members  reduce  the  cost  of  insur- 
ance and  render  it  practicable  to  charge  a  small  net 
premium?  As  in  the  case  of  the  preceding  topic,  we 
have  space  to  answer  only  briefly  now,  but  will  explain 
more  fully  in  a  later  chapter. 

We  assumed  that  there  would  be  no  new  members, 
chiefly  to  simplify  the  matter  of  computation,  but  it  is 
also  true  that  each  age  must  bear  its  own  natural  cost, 
that  the  addition  of  new  members  is  not  essential  to  the 
successful  career  of  a  well-established  company,  and  that 
such  additions  cannot  affect  the  amount  of  premium 
mathematically  necessary. 

Turn  again  to  the  mortality  table.  Notice  that 
at  age  fifty  there  are  69,804  of  the  original  100,000 
persons  still  living.  Assume,  now,  the  organization  of 
another  company  of  69,804  members  all  fifty  years  of 
age,  and,  by  the  method  of  computation  heretofore  illus- 
trated you  will  find  the  net  annual  premium  at  that 

28 


age  to  be  $36.36.  This  is  the  net  amount  mathemati- 
cally necessary  for  each  member  entering  such  a  com- 
pany at  age  50  to  pay  yearly  during  life  to  enable  the 
company  to  pay  all  policies  as  they  mature  by  death. 

Can  the  net  annual  premium  of  $47.76  charged 
by  our  hypothetical  company  for  members  fifty-six  years 
of  age  be  reduced  by  the  addition  of  "  new  blood  " — ^the 
influx  of  younger  men,  say  for  example,  the  addition  to 
our  original  company  of  69,804  new  members,  all  fifty 
years  of  age?  We  have  seen  that  the  net  annual  pre- 
mium mathematically  necessary  at  age  fifty  is  $36.36. 
If  the  payments  of  these  younger  men  are  to  be  applied 
in  part  to  reducing  the  cost  of  the  insurance  to  the  older 
members,  there  will  certainly  be  a  deficit  in  their  own 
funds  unless  their  own  premium  of  $36.36  is  correspond- 
ingly increased.  But  to  make  such  an  increase  would  not 
be  equity.  To  charge  one  set  of  members  more  than 
mathematical  cost  in  order  to  furnish  another  class  with 
insurance  at  less  than  cost  would  be  monstrous.  All 
schemes  of  life  insurance  based  upon  that  idea — ^the  as- 
sessment plan — have  ended  or  must  inevitably  end  in 
failure. 


29 


chapter  iv 
The  Different  Kinds  of  Policies 

Ordinary  Life  and  Limited  Payment  Life  Contracth 

So  far  we  have  treated  only  of  the  ordinary  life 
policy,  a  contract  payable  at  death,  with  equal  annual 
premiums  to  be  paid  during  the  lifetime  of  the  insured. 
It  is,  however,  often  desirable  to  complete  the  payment 
of  all  premiums  within  a  limited  period,  say  within  ten 
or  fifteen  or  twenty  years.  A  policy  payable  only  at 
death  but  which  is  fully  paid  for  in  a  limited  number  of 
premiums  is  termed  a  Limited-Payment  Life  Policy. 
Thus,  when  but  ten  premiums  are  to  be  paid,  we  have  a 
Ten-Payment  Life.  If  twenty  premiums  are  called  for, 
the  contract  is  a  Twenty-Payment  Life,  etc. 

If  the  reader  has  not  thoroughly  mastered 
Chapters  II  and  III,  he  will  do  well  to  study  them  again 
with  care  before  going  further.  The  net  single  premium 
of  a  life  policy  issued  at  age  fifty-six  has  been  shown  in 
Chapter  II  to  be  $621.18.  Dividing  this  amount  by  the 
value  of  a  life  annuity  of  $1.00  issued  at  the  same  age, 
we  obtain  the  net  yearly  premium  payable  during  life. 
To  apportion  the  net  single  premium  into  a  limited 
number  of  equivalent  payments,  as  for  example,  ten,  or 
twenty,  is  an  equally  simple  process,  the  divisor  in  the 
case  being  the  value  of  a  temporary  annuity  running 
for  a  like  period  of  10  or  20  years  instead  of  by  the  value 
of  a  life  annuity. 

90 


Determining  the  Limited  Payment  Premium 
A  Temporary  Annuity  is  one  which,  like  a  life 
annuity,  terminates  on  the  death  of  the  annuitant,  but 
which,  unlike  the  latter,  must  terminate  also  when  a 
specified  number  of  payments  have  been  received,  as  ten 
or  twenty,  even  though  the  annuitant  be  still  living.  To 
determine  the  net  yearly  premium  of  a  ten-payment  life, 
divide  the  net  single  premium  of  a  life  policy  by  the  value 
of  a  temporary  annuity  of  $1.00  terminating  in  ten  years. 
The  net  yearly  premium  of  a  twenty-payment  life  is 
likewise  found  by  dividing  the  net  single  premium  of  a 
life  policy  by  the  value  of  a  twenty  year  temporary 
annuity. 

Computation  of  Temporary  Annuity 

The  value  of  a  temporary  annuity  is  computed 
by  a  process  similar  to  that  followed  in  the  case  of  a  life 
annuity.  Assume,  for  example,  that  every  member  of 
our  hypothetical  company  (page  12),  is  to  receive  a  tem- 
porary annuity  of  $1.00  at  the  beginning  of  every  year 
for  ten  years.  Turn  now  to  the  illustration  on  page  23 
The  present  worth  of  the  amount  required  to  make  an 
immediate  payment  of  $1.00  to  each  of  63,364  persons 
would  be  $63,364.  The  present  worth  of  the  amount 
required  to  pay  the  annuities  of  the  second  year  at  age 
fifty-seven  would  be  $60,295.15.  The  present  worth  of 
the  amount  required  for  the  tenth  year  at  age  sixty-five 
would  be  $37,815.77.  The  student  will  readily  calculate 
the  present  worth  of  the  amounts  required  to  pay  the 
annuities  of  each  of  the  intervening  years.     The  sum  of 

81 


all  these  present  worths  from  the  first  year  to  the  tenth 
inclusive,  will  be  the  total  present  fund  required  to 
enable  the  company  to  pay  the  annuities  of  the  entire 
ten  years.  Dividing  this  sum  by  the  original  number  of 
annuitants,  to  wit:  63,364,  will  give  us  the  value  of  a 
temporary  annuity  of  $1.00,  granted  at  age  fifty-six,  and 
terminating  with  the  tenth  payment.  The  value  of  a 
twenty-year  temporary  annuity  of  $1.00  may  be  ascer- 
tained in  the  same  manner. 

Term  Insurance 

Men  sometimes  desire  temporary  life  insurance 
for  the  sake  of  protection  during  a  specified  period  pend- 
ing the  development  of  a  business  enterprise,  the  maturity 
of  a  debt,  the  dependence  of  minor  children,  etc.  Sup- 
pose, for  example,  that  the  insurance  is  taken  for  ten 
years  instead  of  for  the  whole  of  life.  If  the  insured  dies 
within  the  period  named  his  policy  will  be  paid.  If  he 
lives  longer  than  ten  years,  the  insurance  terminates — 
the  contract  is  of  no  further  validity. 

This  is  called  Term  Insurance.  A  Term  Policy 
is  one  which  is  payable  only  at  death  and  then  only  on 
condition  that  death  occurs  within  a  stated  period — ^the 
term  for  which  the  contract  is  written.  A  contract  cover- 
ing a  period  of  ten  years  is  a  Ten-Year  Term  Policy.  In 
the  same  way  we  have  a  One-Year  Term,  a  Twenty-Year 
Term,  a  Thirty-Year  Term,  etc. 

Such  a  policy  is  sometimes  renewable  for  one 
or  more  periods  at  a  correspondingly  higher  rate,  but 
without  regard  to  the  physical  condition  of  the  insured. 


This  is  Renewable  Term  Insurance,  and  we  have  accord- 
ingly a  Yearly  Renewable  Term,  a  Ten-Year  Renewable 
Term,  etc.  A  renewable  term  policy  may,  nevertheless, 
by  stipulation  in  the  contract  finally  terminate  at  a  fixed 
date.  For  example,  we  may  have  a  ten-year  renewable 
term  "terminating  at  age  seventy."  Term  insurance  in 
The  Mutual  Life  is  not  renewable  save  in  the  case  of  the 
"yearly  renewable  term",  which  expires  at  age  65  but 
may  then  be  changed  to  ordinary  life  with  premium 
corresponding  to  attained  age. 

The  discontinuance  of  a  term  policy  at  the  com- 
pletion of  the  period  for  which  it  was  written  is  called  a 
Termination  by  Expiry, 

Determining  the  Premium  of  a  Term  Policy 

The  process  of  computing  the  premium  of  a  term 
policy  will  be  readily  understood.  Let  us  assume,  for 
example,  that  the  members  of  our  hypothetical  company 
(page  12),  are  all  insured  for  a  term  of  only  ten  years 
instead  of  for  the  whole  of  life.  With  63,364i  persons 
insured  at  age  fifty-six,  we  shall  have  the  death  claims  of 
the  first  ten  years  only  to  pay.  The  47,361  persons 
living  beyond  that  period,  although  they  have  paid 
premiums  for  ten  years,  will  receive  nothing.  Turning 
to  page  1 8,  we  note  that  the  present  worth  of  the  amount 
required  to  pay  the  losses  of  the  firstyear  is  $1,223,300.98. 
In  like  manner  the  present  worth  of  the  amount  required 
for  the  tenth  year  is  $1,473,305.94.  From  explanations 
heretofore  given,  the  reader  will  be  able  to  compute  the 
present  worth  of  the  several  amounts  required  for  the 

83 


intervening  years.  The  sum  of  the  present  worths  of  the 
first  ten  years  will  be  the  total  insurance  fund  necessary 
to  have  on  hand  at  the  beginning  to  enable  the  company 
to  pay  all  the  losses  of  ten  years,  and  this  amount  divided 
by  the  whole  number  of  insured  lives,  to  wit:  63,364, 
will  give  us  the  net  single  premium  of  a  ten-year  term 
policy  at  age  fifty-six  by  the  American  Experience 
Table  and  three  per  cent,  interest.  Dividing  the  net 
single  premium  by  the  value  of  a  ten-year  temporary 
annuity  of  $1.00  (see  page  31),  will  give  us  the  net 
annual  premium  required 


So-called  "Profits"  in  Life   Insurance 

The  holder  of  a  term  policy  who  lives  beyond  the 
end  of  the  period  for  which  the  contract  was  written,  has 
paid  simply  for  protection  during  that  period.  There  is 
nothing  more  coming  to  him  for  the  premiums  he  has 
expended,  yet  he  is  neither  gainer  nor  loser  by  the  trans- 
action. He  has  received  the  protection  for  which  he 
paid,  and  has  had  it  at  exact  cost. 

The  company  which  pays  a  loss  of  $1,000  in  the 
first  year,  having  received  from  the  deceased  but  one 
yearly  premium  of  possibly  $39.26,  is  neither  gainer  nor 
loser  by  the  transaction.  It  insures  63,S64i  persons  for  a 
period  of  ten  years,  and  during  fhose  ten  years  it  collects 
from  the  insured  members  the  exact  amount  of  money 
necessary  for  the  payment  of  all  losses,  according  to  its 
computation  based  upon  the  mortality  table  and  the  as- 
sumed rate  of  interest,  plus  the  necessary  loading  for 

84 


expenses.  It  is  immaterial  to  the  company  whether  this 
member  or  that  member  lives  or  dies;  the  total  death 
claims  cannot  exceed  a  certain  amount,  and  for  the  pay- 
ment of  those  claims  the  company  has  collected  the  exact 
mathematical  cost. 

All  this  is  equally  true  of  the  ordinary  life  policy, 
the  limited  payment  policy,  and  of  every  other  form  of 
contract  written,  all  alike  being  based  upon  exact  mathe- 
matical cost.  In  life  insurance  there  can  be  neither  gain 
nor  loss,  to  company  or  policy-holder,  so  long  as  the 
mortality  corresponds  with  that  of  the  table,  the  interest 
received  with  the  assumed  rate,  and  the  expense  of 
management  and  outlay  for  contingencies  with  the  provi- 
sion made  therefor  in  the  loading. 

In  practice,  however,  there  are  gains  in  the  case 
of  every  well-managed  company.  If,  by  reason  of  a 
careful  selection  of  insured  lives,  the  mortality  is  less 
than  that  indicated  by  the  table  upon  which  the  pre- 
miums were  based,  the  difference  will  be  so  much  gain. 
Our  hypothetical  company  anticipated  16,003  deaths  in 
the  course  of  its  first  ten  years,  as  indicated  by  the 
mortality  table,  and  accordingly  made  provision  in  its 
premium  charge  for  the  payment  of  $16,003,000  in 
claims  during  that  time.  Had  its  actual  mortality  proved 
to  be  but  seventy-five  per  cent,  of  that  amount  there 
would  have  been  a  considerable  gain  in  the  saving  thus 
effected.  Such  gains  are  not  uncommon  in  practice.  Most 
companies  have  an  average  mortality  of  not  more  than 
eighty  or  ninety  per  cent,  of  that  shown  by  the  table.  A 
well-managed  company  will  likewise  make  gains  from 
interest  received  in  excess  of  the  assumed  rate,  and  from 

35 


the  saving  effected  by  incurring  smaller  expenses  than 
the  amount  collected  for  that  purpose — all  of  which  will 
be  treated  of  in  a  later  chapter. 

To  Whom  the  Profits  Go 

Bear  in  mind  that  in  the  case  of  a  stock  life 
insurance  company  (see  page  6)  the  gains  and  savings 
thus  effected  all  belong  to  the  stockholders.  In  the  case 
of  a  mixed  company — that  is^  a  stock  company  doing 
business  on  the  mutual  plan  (page  7)^  a  part  of  the 
savings  go  to  the  stockholders  and  the  balance  to  the 
policy-holders.  In  a  purely  mutual  organization,  such 
as  The  Mutual  Life  Insurance  Company  of  New  York  in 
which  there  are  no  stockholders,  every  dollar  gained 
from  first  to  last  belongs  to  the  policy-holders  and  will 
be  returned  to  them  when  the  apportionment  of  surplus  is 
made  in  accordance  with  their  several  contracts.  This 
subject  will  be  more  thoroughly  discussed  in  a  later 
article  under  the  head  of  Surplus. 

Endowment  Policies 

A  man  may  wish  to  make  some  provision  for  his 
own  future  in  addition  to  providing  for  his  dependents. 
To  this  end  Endowment  Insurance  has  been  devised. 
The  Endowment  Policy  is  one  which  is  payable  to  the 
insured  himself  if  he  lives  through  a  specified  number  of 
years  or  to  a  stated  age,  but  payable  to  his  legal  repre- 
sentatives or  beneficiary  in  the  event  of  his  prior  death. 
Thus  a  policy  payable  to  the  insured  himself  if  living  at 
the  end  of  twenty  years,  but  to  his  beneficiary  in  case  of 

86 


his  prior  death,  is  a  Twenty-Year  Endowment,  In  like 
manner  we  have  a  Fifteen-Year  Endowment,  a  Thirty- 
Year  Endowment,  etc. 

Such  a  policy  is  a  combination  of  term  insurance 
and  what  is  known  as  Pure  Endowment,  The  latter 
form  of  policy  is  payable  only  to  those  who  live  to  com- 
plete the  endowment  period.  Those  who  die  prior  to 
that  date  receive  nothing.  This  is  purely  "investment 
insurance." 

Assume,  for  example,  the  issue  of  a  ten-year 
Pure  Endowment  for  $1,000  to  each  of  the  63,364. 
members  of  our  hypothetical  company  at  age  fifty-six. 
During  the  next  ten  years  16,003  members  will  die. 
These  receive  nothing.  There  will  be  47,361  survivors 
who  are  to  receive  $1,000  each,  requiring  a  total  pay- 
ment of  $47,361,000.  The  present  worth  of  that  sum 
at  three  per  cent.,  to  wit:  $35,241,031.67,  represents 
the  total  insurance  fund  required  at  the  beginning. 
This  amount  divided  by  the  total  number  insured,  63,364, 
gives  $556.17,  the  net  single  premium  of  a  ten-year 
pure  endowment  at  age  fifty-six  by  the  American 
Experience  Table  and  three  per  cent,  interest.  That  is 
to  say,  if  63,364  persons  at  age  fifty-six  contribute  each 
the  sum  of  $556.17,  the  fund  will  be  just  sufficient,  with 
the  aid  of  three  per  cent,  interest,  to  pay  $1,000  to  each 
of  the  47,361  members  who  survive  the  period. 

The  Endowment  Premium, 

Keep  in  mind  the  fact  that  the  holder  of  a  pure 
endowment  policy,  who  dies  before  completion  of  the 
endowment  period,  receives  nothing.     If,  however,  each 

37 


of  our  63,364!  members  carries  also  term  insurance 
covering  the  same  period,  then  each  one  of  the  16,003 
who  die  will  likewise  receive  his  $1,000.  Thus  by 
combining  the  premium  of  a  lerm  policy  with  that  of 
a  pure  endowment,  we  obtain  the  premium  of  the  regular 
endowment,  which  provides  for  both  those  who  die  and 
those  who  live.  This  may  be  illustrated  as  follows :  The 
net  single  premium  for  a  ten-year  term  policy  of  $1,000 
at  age  fifty-six  is  $212.80,  while  the  corresponding  net 
single  premium  for  a  pure  endowment,  as  already  shown, 
is  $556.17.  The  former  provides  for  all  who  die  within 
the  ten  years ;  the  latter  for  all  who  are  still  living  at  the 
end  of  that  time.  Combining  the  two  we  get  $768.97, 
which  is  the  net. single  premium  of  a  regular  ten-year 
endowment. 

Reverting  again  to  the  pure  endowment,  written 
as  a  separate  contract;  observe  that  the  net  single  pre- 
mium of  $556.17  at  three  per  cent,  compound  interest, 
will  amount  in  ten  years  to  only  $747.44  instead  of  to 
$1,000.  The  difference  is  made  up  by  the  premiums 
forfeited  by  the  16,003  members  who  die  during  the 
term  and  receive  nothing. 

Effect  of  Mortality  in  Endowment  Insurance 

The  pure  endowment  net  single  premium  of 
$556.17  is  based  upon  the  expectation  that  the  mortality 
will  be  the  same  as  that  indicated  by  the  table.  If 
there  were  no  deaths  at  all  during  the  ten  years,  en- 
titling every  one  of  our  63,364  members  to  an  endow- 
ment of  $1,000  at  the  end  of  the  period,  the  net  single 


premium  for  each  one  to  pay  would  be  $744.09,  that 
being  the  sum  which  at  three  per  cent,  compound  in- 
terest would  amount  to  $1,000  in  that  time.  That  is,  if 
there  were  no  deaths  at  all  during  the  ten  years,  a  net 
single  premium  of  only  $556.17  would  leave  a  large 
deficit.  Likewise,  it  is  obvious  that  if  there  were  fewer 
deaths  than  indicated  by  the  table,  there  would  be  more 
endowments  to  pay  than  were  counted  upon,  and  again 
there  would  be  a  deficit.  On  the  other  hand,  if  the 
deaths  were  to  exceed  the  mortality  table,  there  would 
be  fewer  endowments  to  pay  than  were  anticipated,  and 
this  would  result  in  a  corresponding  gain.  In  other 
words,  in  pure  endowment  insurance,  the  higher  the 
mortality  rate,  the  larger  the  gains  to  the  company, 
while  a  mortality  less  than  that  of  the  table  must  result 
in  actual  loss.  The  reverse  of  this  is  found  in  term 
insurance,  where  the  lower  the  mortality,  the  better  for 
the  company.  By  combining  the  two  forms,  the  favorable 
effect  of  a  low  mortality  in  term  insurance  more  than 
counteracts  the  adverse  effect  of  the  same  condition  in 
pure  endowment. 


89 


chapter  v 

Proving  the  Adequacy  of  the 
Net  Premium 

IF  the  reader  has  studied  Chapters  II  and  III  with  care, 
he  is  convinced  of  the  correctness  of  the  process  by 
which  the  net  yearly  premium  at  age  fifty-six  is  com- 
puted, and  will  readily  comprehend  that  by  a  like  process 
the  necessary  net  premium  at  any  other  age  may  be 
ascertained.  At  the  same  time,  a  mathematical  verifica- 
tion of  the  work  may  serve  to  fix  the  principle  involved 
more  firmly  in  his  mind,  and  to  emphasize  more  forcibly 
the  certainty  of  the  life  insurance  proposition. 

For  example,  by  mathematical  computation  we 
have  found  the  net  annual  premium  of  an  ordinary  life 
policy  of  $1,000  at  age  fifty-six,  American  Experience 
Table  and  three  per  cent,  interest,  to  be  $47.76. 
Referring  again  to  our  hypothetical  company,  page  12, 
we  may  prove  the  exact  sufficiency  of  that  premium  by 
"working  it  out,"  computing  the  amount  of  premiums 
received  the  first  year,  adding  interest  assumed,  deducting 
claims  paid,  adding  balance  to  premium  income  of  the 
second  year,  improving  the  sum  at  interest,  deducting 
claims,  etc.,  until  the  premiums  of  the  last  three 
members  have  been  collected  in  the  fortieth  year,  and 
their  policies  paid. 

It  should  be  explained  here  that  inasmuch  as 
computations  in  life  insurance,  as  in  other  sciences,  in- 
volve the  use  of  decimals,  exact  results  are  not  attainable. 
For  example,  we  have  had  occasion  on  page  17  to  find 
the  present  worth  of  $1,980,000,  due  in  ten  years,  at 

40 


three  per  cent,  interest.  Now  the  present  worth  of  $1.00 
on  the  terms  named  would  be  $0.74,  or,  carrying  it  to 
three  decimal  places,  $0,744;  that  is,  seventy-four  cents 
and  four  mills.  Carried  to  five  decimals  we  should  have 
$0.74409;  six  places,  $0.744094.  If  we  regard  the 
present  worth  of  $1.00  as  $0.74,  then  the  present  worth 
of  $10.00  would  be  $7.40;  but  if  we  use  three  decimals 
($0,744),  we  get  $7.44  as  the  present  worth  of  $10.00 
instead  of  $7.40.  Again  if  the  present  worth  of  $1.00 
is  $0,744  the  present  worth  of  $1,000  would  be  $744.00; 
but  if  we  use  five  decimals  in  the  present  value  of  $1.00 
(to  wit  $0.74409)  we  shall  have  $744.09  as  the  present 
worth  of  $1,000  instead  of  $744.00.  It  will  be  readily 
seen  that  the  assumed  present  worth  of  a  large  sum  like 
$1,980,000  will  vary  materially  according  to  the  number 
of  decimal  places  employed  in  the  computation.  Three 
decimals  in  the  present  worth  of  $1.00  (to  wit  $0,744) 
would  give  us  $1,473,120.00  as  the  present  worth  of 
$1,980,000,  while  six  decimals  ($0.744094)  would  give 
us  $1,473,306.12,  and  the  still  larger  number  of  decimals 
employed  in  our  computation  gave  us  $1,473,305.94  as  a 
more  nearly  accurate  result.  It  will  be  seen  that  in 
computations  involving  vast  amounts,  the  greater  the 
number  of  decimal  places  used  the  nearer  will  be  the 
approach  to  actual  accuracy.  In  compiling  the  Verifica- 
tion Table  appearing  in  this  chapter  more  decimal  places 
were  employed  than  is  usual  in  ordinary  work  because  of 
the  great  number  of  dependent  computations  involved. 
This  explanation  is  made  for  the  benefit  of  anyone  who 
may  find  difficulty  in  verifying  exactly  the  figures  given 
herein. 

41 


The  Exact  Net  Premium 

The  net  premium  of  $47.76  given  above  is  the 
amount  actually  collected  in  practice,  though  a  more 
nearly  correct  premium,  carried  to  six  decimal  places, 
would  be  a  fraction  of  a  cent  more  than  that,  to  wit: 
$47.760895. 

The  proposition  now  is  to  prove  that  this  net 
premium  of  $47.760895  is  a  sufficient  charge  for  an  ordi- 
nary life  policy  of  $1,000  at  age  fifty-six.  If  this  can  be 
shown  it  will  be  conceded  that  by  the  same  process  the 
adequacy  of  the  net  premium  charge  at  other  ages  can  be 
proved.  In  practice  it  is  not  possible  to  collect  the 
fractional  part  of  the  cent  ($.000895),  less  than  one-tenth, 
as  we  have  assumed  to  do  in  the  Verification  Table, 
but  the  slight  deficit  resulting  therefrom  in  large  trans- 
actions is  easily  adjusted  with  gains  from  other  sources. 

It  might  be  well  to  repeat  here  that  the  gross 
premium  in  life  insurance  is  composed  of  two  parts,  the 
net  premium  and  the  loading.  The  net  premium,  with 
which  alone  we  have  to  do  at  present,  is  devoted  solely 
to  the  payment  of  policy  claims.  No  part  of  it  can  be 
used  for  any  other  purpose.  The  loading  is  an  amount 
arbitrarily  added  to  the  net  premium  for  payment  of 
expenses  not  otherwise  provided  for,  and  for  other  con- 
tingencies, and  does  not  affect  the  question  of  the 
mathematical  sufficiency  of  the  net  premium. 

We  have  already  stated,  page  14,  that,  while  in 
practice  death  claims  may  be  paid  at  any  time,  yet, 
theoretically,  they  are  all  payable  at  the  end  of  the  year. 
It  is  upon  this  basis  that  the  net  premium  is  computed, 
and  to  prove  the  correctness  of  the  computation,  there- 

42 


fore,   the   same  hypothesis   must  be  adopted, — ^that   all 
death  claims  are  payable  at  the  end  of  the  year. 

Our  hypothetical  company  has  63,364  members 
as  stated.  Collecting  from  each  of  these  the  sum  of 
$47.760895,  gives  us  a  net  premium  income  for  the 
first  year  of  $3,026,321.35.  To  this  we  add  twelve 
months'  interest  at  three  per  cent.  ($90,789.64),  which 
makes  our  total  income  $3,117,110.99.  By  turning  to 
the  mortality  table  (page  13),  we  note  that  at  age  fifty- 
six  we  shall  have  1,260  deaths  during  the  year,  calling 
for  the  payment  of  claims  to  the  amount  of  $1,260,000. 
Deducting  these  death  claims  from  the  total  income,  we 
get  a  balance  of  $1,857,110.99.  The  operations  of  the 
year  may  be  tabulated  in  the  following  manner: 

Net  premium  income  beginning 

of  the  year $3,026,321.35 

Add  one  year's  interest  (three 

per  cent.)    90,789.64 

Total  income  first  year $3,117,110.99 

Deduct   death   claims 1,260,000.00 

Balance  end  of  first  policy  year     $1,857,110.99 
The  Reserve 

Study  the  above  figures.  Note  that  the  net 
premium  income,  increased  by  one  year's  interest  thereon 
at  the  assumed  rate  (three  per  cent.),  constitutes  our  total 
insurance  fund.  This  might  be  termed  the  Mortality 
Fund,  but  the  expression  has  not  obtained  in  regular  life 
insurance,  the  term  Reserve  being  in  universal  use.  The 
Reserve  includes  all  funds  in  life  insurance  devoted  to 
the  payment  of  policy  claims — that  is,  the  net  premium 

43 


receipts  and  the  interest  earned  on  those  receipts  to  the 
extent  of  the  assumed  rate  (three  per  cent.).  The 
balance  of  the  insurance  fund  on  hand  at  the  end  of  the 
policy  year,  after  deducting  policy  claims,  is,  for  the  sake 
of  distinction,  called  the  Terminal  Reserve;  while  the 
fund  on  hand  at  the  beginning  of  the  year  (consisting  in 
the  first  year  of  the  net  premium  income  only),  is  termed 
the  Initial  Reserve, 

If  the  terminal  reserve  in  the  above  case 
($1,857,110.99)  be  divided  by  62,104,  the  number  of 
members  still  living  (see  page  60),  we  shall  obtain 
$29.90,  which  is  the  terminal  reserve  pertaining  to  each 
policy  still  in  force  at  the  end  of  the  first  year. 

At  the  commencement  of  the  second  policy  year 
we  have  62,104  persons  living  at  the  attained  age  of 
fifty-seven  years.  Each  of  these  pays  the  same  net 
premium  as  before,  making  our  total  premium  income 
at  the  beginning  of  the  second  year,  $2,966,142.62. 
Adding  to  this  the  amount  reserved  from  the  preceding 
year  ($1,857,110.99,  see  table  of  operations  first  year, 
page  43),  we  now  have  an  insurance  fund  of 
$4,823,253.61,  which  is  the  initial  reserve  of  the  second 
year.  Again  we  add  to  this  sum  one  year's  interest  at 
three  per  cent.,  to  wit:  $144,697.61,  and  we  get  a  total 
fund  for  the  second  year  of  $4,967,951.22.  Deducting 
from  this  the  death  claims  of  the  year  according  to  the 
mortality  table,  to  wit:  $1,325,000,  we  have  a  balance 
of  $3,642,951.22,  which  is  the  terminal  reserve  at  the 
end  of  the  second  policy  year.  If  this  amount  be  divided 
by  60,779,  the  number  of  members  still  living,  we  shall 
get  $59.94,  which  is  the  terminal  reserve  pertaining  to 

44 


i 


each  policy  at  the  end  of  the  second  year.  The  operations 
of  the  year  may  be  tabulated  in  the  following  manner: 

Net    premium    income    second 

year     $2,966,142.62 

Add  terminal   reserve   of   pre- 
ceding year    1,857,110.99 

Total    beginning    second    year 

(initial  reserve)    $4,823,253.61 

Add  one  year's  interest  (three 

per  cent.)    144,697.61 

Total  end  of  second  year $4,967,951.22 

Deduct  death  claims 1,325,000.00 

Balance    end   of    second   year, 

(terminal  reserve)    $3,642,951.22 

A  Verification  Table 
The  complete  solution  of  the  problem — ^the  proof 
of  the  sufficiency  of  the  net  yearly  premium  is  illustrated 
in  the  annexed  figures  which,  for  convenience  of  refer- 
ence, we  have  termed  a  Verification  Table.  Column  four 
gives  the  net  premium  income  for  each  year.  Column 
five  shows  the  initial  reserve,  consisting  (after  the  first 
year),  of  the  net  premium  income  plus  the  terminal 
reserve  of  the  preceding  year.  To  the  sum  of  these  is  to 
be  added  one  year's  interest  which  is  set  out  in  column 
six.  From  this  amount  (not  entered  in  the  table  for  lack 
of  room)  will  be  deducted  the  death  claims  of  the  year  as 
indicated  by  the  mortality  table  and  shown  in  column 
seven.  The  balance  (column  eight),  will  be  the  terminal 
reserve  for  the  year.  This  divided  by  the  number  of 
members  still  living  (see  column  two,  next  higher  age), 
will  give  the  terminal  reserve  pertaining  to  each  policy, 
as  shown  in  column  nine. 

45 


Ordinary  Life,  $1,000 


Age  56 


VERIFICATIOl 
Net  Year] 


1 

2 

3 

4 

5 

Age 

Members 
Living 

Deaths 

Net  Premium 
Income 

Initial  Reserve 

56 
67 

58 
69 
€0 

63,364 
62,104 
60,779 
59,385 
57,917 

1,260 
1,325 
1,394 
1,468 
1,546 

$3,026,321  35 
2,966,142  62 
2,902,859  44 
2,836,280  75 
2.766,167  76 

$3,026,321  35 
4,823,253  61 
6,545,810  66 
8,184,465  73 
9.728.167  46 

61 
62 
63 
64 
65 

56,371 
54,743 
53,030 
51,230 
49,341 

1,628 
1,713 
1,800 
1,889 
1,980 

2,692,329  41 
2,614,574  67 
2,532,760  26 
2,446,790  65 
2,356,570  32 

11.166,341  89 
12,487,906  82 
13,682,304  28 
14,739,564  06 
15,649,321  30 

66 
67 
68 
69 
70 

47,361 
45,291 
43,133 
40,890 
38,569 

2,070 
2,158 
2,243 
2,321 
2,391 

2,262,003  75 
2,163,138  70 
2,060,070  68 
1,952,943  00 
1.842,089  96 

16,400,804  69 
16,985,967  53 
17,397,617  24 
17,629,488  76 
17.679,463  38 

71 

72 
73 

74 
75 

38,178 
33,730 
31,243 
28,738 
26,237 

2,448 
2,487 
2,505 
2,501 
2,476 

1,727,894  16 
1,610,975  50 
1,492,194  14 
1,372,553  11 
1,253,103  10 

17,546,741  44 
17,236,119  18 
16,758,396  90 
16,128,701  92 
15,364,666  08 

76 

77 
78 
79 
80 

23,761 
21,330 
18,961 
16,670 
14,474 

2,431 
2,369 
2,291 
2,196 
2,091 

1,134,847  14 

1,018,740  39 

905,595  84 

796,174  87 

691.291  19 

14,484,453  20 
13,506,727  19 
12,448,524  85 
11,327,155  47 
10,162,261  32 

81 

82 
S3 

84 
85 

12,383 

10,419 

8,603 

6,955 

5,485 

1,964 
1,816 
1,848 
1,470 
1,292 

591,423  16 
497,620  77 
410,886  98 
332,177  02 
261,968  51 

8,967,552  32 
7,770,199  66 
6,598.192  63 
5,480,315  43 
4.436.693  40 

86 
87 
88 
89 
90 

4,193 
3,079 
2,146 
1,402 
847 

1,114 
933 
744 
555 
385 

200.261  43 

147.055  80 

102,494  88 

66,960  77 

40,453  48 

3,478,055  63 
2,615,453  10 
1,863,411  57 
1,242,274  69 
764,996  41 

91 
92 
93 
94 
95 

462 

216 

79 

21 

3 

246 

137 

58 

18 

3 

22,065  53 

10,316  35 

3,773  11 

1,002  98 

143  28 

425,011  83 

202,078  54 

74,914  01 

20,164  41 

2.912  62 

\BLE 

remium  $47.760895 


American  Experience  3  Per  Cent 


6 

7 

8 

9 

10 

Add 

One  Year's 

Interest 

Deduct 
Death  Claims 

Balance, 
Terminal  Reserve 

Reserve 
on  each  Policy 

Endo! 

$90,789  64 
144,697  61 
196,374  32 
245,533  97 
291,845  02 

$1,260,000 
1,325,000 
1,394,000 
1,468,000 
1,546,000 

$1,857,110  99 
3,642,951  22 
5,348,184  98 
6,961.999  70 
8,474,012  48 

$29  90 

59  94 

90  06 

120  21 

150  33 

lYr. 
^Yrs. 

3  " 

4  " 

334,990  26 
374,637  20 
410,469  13 
442,186  92 
469,479  64 

1,628,000 
1,713,000 
1,800,000 
1,889,000 
1,980,000 

9,873,332  15 
11,149,544  02 
12,292,773  41 
13,292,750  98 
14,138,800  94 

180  36 
21025 
239  95 
269  41 
298  53 

6  " 

7  " 

8  " 

9  " 
10  " 

492,024  14 
509,579  03 
521,928  52    . 
528,884  66 
530,383  90 

2,070,000 
2,158,000 
2,243,000 
2,321,000 
2,391,000 

14,822,828  83 
15,337,546  56 
15,676,545  76 
15.837,373  42 
15,818,847  28 

327  28 
355  59 
383  38 
410  62 
437  25 

:/!  " 

12  " 

13  " 

14  " 

15  " 

526,402  24 
517,083  58 
502,751  91 
483.861  06 
460,939  98 

2,448,000 
2,487,000 
2,505,000 
2,501.000 
2,476,000 

15,625,143  68 
15,266,202  76 
14,756,148  81 
14,111,562  98 
13.349,606  06 

463  24 
488  63 
51347 
537  85 
561  83 

16  " 

17  " 

18  " 

19  " 

20  " 

434,533  60 
405,201  82 
373,455  75 
339,814  66 
304,867  84 

2,431,000 
2,369,000 
2,291,000 
2,196,000 
2,091,000 

12,487,986  80 

11,542,929  01 

10,530,980  60 

9,470,970  13 

8,376,129  16 

585  47 
608  77 
631  73 
654  34 
676  42 

21  " 

22  " 

23  " 

24  " 

25  " 

269,026  57 
233,105  99 
197,945  78 
164,409  48 
133,100  80 

1,964,000 
1,816,000 
1,648,000 
1,470,000 
1.292,000 

7,272,578  89 
6,187,305  65 
5,148,138  41 
4,174,724  89 
3,277,794  20 

698  01 
71920 
740  21 
761  12 
781  73 

26  '^ 

27  " 

28  " 

29  " 

30  " 

104,341  67 
78,463  59 
55,902  35 
37,268  24 
22,949  89 

1,114,000 
933,000 
744,000 
555,000 
385,000 

2,468,397  30 

1,760,916  69 

1,175,313  92 

724,542  93 

402,946  30 

801  69 
820  56 
838  31 
855  42 
872  18 

31  " 

32  " 

33  " 

34  " 

35  " 

12,750  36 

6,062  36 

2,247  42 

604  93 

87  38 

246,000 

137,000 

58,000 

18,000 

3,000 

191,762  19 

71,140  90 

19,161  43 

2.769  34 

887  79 
900  52 
912  45 
923  11 

36  " 

37  " 

38  " 

39  " 

40  " 

47 


By  means  of  the  table  one  can  quickly  follow  the 
process  through  and  see  for  himself  that  the  net  premium 
is  precisely  adequate.  The  figures  assume  the  collection 
of  that  amount  in  each  year  from  each  living  member. 
Interest  at  three  per  cent,  is  included  from  the  first  on 
all  funds  on  hand.  Every  death  claim  is  paid  in  full  as  it 
matures,  according  to  the  mortality  table.  At  ninety-five 
there  are  but  three  members  yet  living.  These  pay  their 
last  premiums  on  that  day,  making  the  total  net  premium 
income  of  that  year  $143.28.  To  this  is  added  the 
terminal  reserve  of  the  preceding  year,  to  wit: 
$2,769.34,  making  an  initial  reserve  for  the  fortieth  year 
of  $2,912.62.  Adding  to  this  one  year's  interest,  to 
wit:  $87.38,  we  get  $3,000,  or  just  sufficient  to  pay  the 
three  remaining  policies  in  full. 

The  Limit  of  Life 

It  is  assumed  in  the  mortality  table  that  the  last 
three  members  remaining  at  age  ninety-five,  will  not  live 
beyond  the  end  of  that  year.  The  premium  having  been 
computed  on  that  basis,  the  total  insurance  fund,  that  is, 
the  reserve,  must  necessarily  equal  the  face  of  the  policy 
at  that  time,  the  end  of  the  fortieth  year,  when  the 
insured  has  reached  the  age  of  ninety-six.  In  other 
words,  the  reserve  is  equal  to  the  face  of  the  policy  at 
the  limit  of  life  which,  by  the  American  Experience 
Table,  is  the  attained  age  of  ninety-six  years — the  age 
when  the  last  man  is  presumed  to  die. 

The  fact  that  in  actual  experience  men  do  some- 
times live  beyond  the  age  of  ninety-six,  is  not  against 
but  in  favor  of  the  sufficiency  of  our  premium.     If,  for 

48 


example,  the  ultimate  limit  of  life  were  in  fact  three- 
score and  ten,  or  four-score  years,  none  ever  living 
beyond  that  period,  our  premium,  computed  on  the  basis 
of  some  attaining  the  age  of  ninety-six,  would  be  insuffi- 
cient. It  will  be  seen  by  the  Verification  Table  (pages 
46  and  47)  that  the  reserve  on  each  policy  at  the  end  of 
twenty-five  years  amounts  to  only  $676.42.  In  other 
words,  if  the  12,383  members  then  remaining  were  all  to 
die  at  that  time,  at  the  attained  age  of  eighty-one  years, 
the  total  funds  on  hand  would  suffice  to  pay  only  $676.42 
on  each  $1,000  policy.  If  on  the  other  hand,  the  three 
members  remaining  at  age  ninety-five  shall  continue  to 
live  beyond  the  attained  age  of  ninety-six, — say  to  one 
hundred  or  longer,  the  fact  will  not  affect  the  result.  The 
reserve  on  hand  is  equal  to  the  face  of  the  policy — there 
can  be  no  failure  to  pay  the  death  claim  when  it  occurs. 

Examples  of  Remarkable  Longevity 

The  American  Experience  Table  indicates  that 
out  of  81,822  persons  living  at  age  35,  only  3  will  still 
be  living  at  age  95,  and  that  none  of  these  will  live 
beyond  the  attained  age  of  96.  The  experience  of 
The  Mutual  Life  has  been  much  better  than  that.  It  is 
commonly  assumed  that  the  average  age  at  date  of  insur- 
ing is  35.  Of  the  470  persons  insured  in  the  first  year 
of  The  Mutual  Life,  2  lived  beyond  the  age  of  96.  In 
that  proportion  (if  each  of  the  470  persons  had  been 
35  years  of  age  at  date  of  insuring),  the  American 
Experience  Table  would  show  348  out  of  81,822  living 
to  age  96,  instead  of  3.     These  data,  however,  are  too 


meager  to  enable  us  to  form  an  accurate  conclusion. 
Taking  larger  figures,  in  the  first  four  years  the  Com- 
pany insured  3,126  persons.  These  have  all  passed 
away,  5  of  them  living  beyond  age  96.  Proportion- 
ately, the  American  Experience  Table,  in  the  case  of 
81,822  persons  at  age  35,  would  show  131  attaining 
the  age  of  96  instead  of  3. 

The  Company  has  already  had  9  policyholders  to 
live  beyond  the  age  of  96  out  of  32,127  insured  in  the 
first  22  years.  As  many  of  those  insured  in  that  time 
are  still  living,  some  of  whom  may  live  beyond  96,  we 
cannot  give  comparative  results  in  figures,  but  it  is  evi- 
dent that  the  mortality  in  The  Mutual  Life  has  been  far 
more  favorable  than  that  indicated  by  the  table.  In  this 
connection  it  must  not  be  overlooked  that  many  of  the 
32,127  policies  issued  in  the  first  twenty-two  years  ter- 
minated by  lapse  or  surrender,  many  term  policies  ended 
by  expiry,  and  many  endowment  policies  matured  before 
the  death  of  the  insured.  We  have  no  record  of  the 
after-lifetime  of  these  policyholders,  some  of  whom 
probably  lived,  or  will  yet  live,  to  age  96. 

The  following  table  is  a  record  of  the  Company's 
experience  up  to  November  3,  1915. 

J^'Mcy  mMv  Date  of  Date  of  Date  of       Ageatif/J,? 

lumber  ^^^^  Birth  Issue  Death  Issue  Yrs.Mos. 

22  Chas.  H.  Booth  Sept.  30,1803  Feb.     7,1843  May  29,1904  39  100  8 

1,506  Robt.  Street...  June  12,1806  June27,1845  Feb.     1,1903  39  96  8 

2,228  Chas.  Rhind..  Feb.    10,1810  Feb.  27,1846  Apr.  23,1908  36  98  2 

8,151  H.  Blanchard.  Apr.      1,1806  Mch.  13,1850  Nov.27,1902  44  96  7 

1,512  Jesse  W.  Hatch  May   20,1812  June  30, 1845  Jan.  24,1910  33  97  8 

458  G.  L.  Newman  July    15,181«  Jan.   24,1844  Oct.   11,1913  28  97  3 

16,534  Jno.  F.  Mesick  June  17,1813  May   13,1856  June30,1915  43  102  — 

13,869  Jno.  P.  Daniels  Apr.   28, 1815  Nov.  25, 1854  Nov.  11,1912  40  97  6 

32,127  Jas.  M.Woltz.  Dec.   14, 1818  May  25, 1864  Nov.     3,1915  45  96  11 

50 


John  P.  Daniels  surrendered  his  insurance  for  the 
face  amount  in  cash  on  attaining  the  age  of  96.  This  is 
a  privilege  always  accorded  by  The  Mutual  Life  to 
policyholders  who  have  lived  to  that  age,  for  the  reserve 
is  equal  to  the  face  amount  of  the  insurance  at  96.  It  is 
a  privilege,   however,   that  has   rarely   been   exercised. 

Since  the  foregoing  matter  was  put  in  type,  an- 
other policyholder,  Judge  Nahum  Morrill,  of  Auburn, 
Maine,  has  attained  the  age  of  96  years,  making  ten 
policyholders  in  all  who  have  passed  the  * 'limit  of  life** 
as  fixed  by  the  American  Experience  Table,  up  to  Decem- 
ber, 1915. 


SI 


chapter  vi 
Observations  on  the  Reserve 

"New  Blood"  not  Essential  to  Permanence 

T  N  the  Verification  Table,  pages  46  and  47:,  we  have  the 
mathematical  proof  that  a  regular  life  insurance  company 
— the  assumptions  as  to  mortality  and  interest  being 
realized— might  cease  writing  new  business  altogether, 
and  by  continuing  to  collect  from  each  member  the 
requisite  mathematical  premium,  would  be  able  to  pay 
all  policies  in  full  including  that  of  the  last  man, — the 
balance  on  hand  when  the  last  policy  matures  at  the 
attained  age  of  ninety-six  being  just  sufficient  for  that 
purpose. 

Reserve  all  for  Mortality  Purposes 

The  Verification  Table  illustrates,  theoretically, 
the  actual  progress  of  a  life  insurance  company  from  the 
beginning  of  its  career  to  the  fulfillment  of  its  last 
contract.  It  illustrates  also  the  fact  that  the  so-called 
Reserve  in  life  insurance  is  simply  the  insurance  fund  or 
mortality  fund  of  the  company,  from  which  all  policy 
claims  are  paid.  Observe  that  at  the  beginning  of  the 
very  first  year  the  initial  reserve,  which  the  company 
under  the  law  must  hold  on  the  day  when  it  commences 
business,  comprises  the  entire  net  premium  income. 
Observe  that  thereafter  the  entire  net  premium  receipts, 
plus  S  per  cent,  interest  thereon  at  the  assumed  rate,  con- 
stitute the  actual  insurance  fund  of  the  company,  always 

62 


designated  as  the  reserve.  Note  that  the  reserve  is  con- 
stantly applied  to  the  payment  of  policy  claims,  until  the 
last  claim  is  met  at  age  ninety-six,  to  which  the  last  dollar 
of  the  net  premium  receipts  and  interest  is  devoted.  In 
other  words,  the  net  premium  is  all  for  mortality  pur- 
poses, or  the  payment  of  policy  claims,  and  for  nothing 
else. 

Some  Popular  Errors 

Several  primary  text  books,  in  attempting  to 
explain  in  a  simple  manner  the  scientific  features  of  life 
insurance,  unwisely  state  that  the  gross  premium  is  com- 
posed of  three  parts,  to  wit:  the  Reserve  Element,  the 
Mortality  Element  and  the  Expense  Element,  The 
statement  is  technically  incorrect  and  has  led  to  much 
confusion.  The  explanation  is  made  that  the  reserve  and 
mortality  elements  combined  constitute  the  net  premium, 
while  by  the  term  "expense  element"  is  meant  the 
loading,  the  three  parts  making  up  the  gross  premium. 

Some  of  these  elementary  writers  have  published 
tabular  exhibits  purporting  to  show  the  division  of  the 
gross  premium  at  the  several  ages  into  mortality,  reserve 
and  expense  elements.  These  apparently  authoritative 
statements  seem  to  indicate,  and  have  been  interpreted 
by  the  uninformed  to  mean,  that  the  so-called  "mortality 
element'*  is  the  estimated  necessary  provision  for  pay- 
ment of  probable  death  claims,  while  the  "reserve 
element"  is  supposed  to  be  purely  an  accumulation  for 
possible  emergencies,  such  as  extraordinary  claims  result- 
ing from  epidemics,  etc. 


Moreover,  the  division  indicated  is  commonly 
understood  to  be  fixed — the  inference  being  that  the 
amounts  apportioned  for  mortality,  reserve,  and  expense 
elements  remain  the  same  in  the  case  of  all  future 
premiums.  Most  promoters  of  assessment  schemes  have 
so  understood  these  figures,  and  many  of  these,  by 
adopting  as  a  net  rate  the  so-called  "mortality  element,'* 
plus  an  addition  of  perhaps  twenty  per  cent,  for  possible 
excess  mortality,  have  loudly  proclaimed  their  conserva- 
tism and  foresight  in  making  a  "larger  provision  for  mor- 
tality" than  is  made  by  the  so-called  "old  line"  compan- 
ies. The  "old  line"  reserve  they  vaguely  designate  as  the 
"investment  element,"  which  is  alleged  to  have  no  place 
in  legitimate  life  insurance.  In  fact,  the  assertion  is 
made  by  the  promoters  of  such  organizations  that  the 
reserve  is  never  drawn  upon  for  the  payment  of  death 
claims.  Even  fairly  well-informed  persons  have  con- 
ceived the  erroneous  notion  that  the  reserve  is  merely  a 
special  fund  pertaining  to  each  policy,  formed  by  the 
accumulation  of  the  "reserve  element"  of  the  premiums 
paid  on  that  policy  at  a  given  rate  of  interest,  and  that 
such  individual  fund  is  never  drawn  upon,  save  as  part 
payment  of  that  particular  policy  when  the  same  becomes 
a  claim. 

Composition  of  the  Premium 

This  aggregation  of  errors  results  largely  from  the 
confusion  caused  by  the  hypothetical  division  of  the  net 
premium  into  reserve  and  mortality  elements.  There  is 
in  reality  no  such  division  save  as  a  bookkeeping  ex- 
pedient, designed  to  facilitate  computations  in  connection 

64 


with  the  apportionment  of  surplus  or  the  solution  of 
similar  problems.  It  is  based  upon  the  fact  that  only  a 
part  of  the  net  premium  income  of  the  earlier  years  is 
required  for  the  payment  of  current  death  claims,  the 
balance  being  reserved  to  meet  future  claims;  wherefore, 
in  an  individual  statement  of  account,  it  has  been  found 
convenient  to  charge  to  mortality  such  proportion  of  the 
net  premium  as  constitutes  its  pro  rata  contribution  to 
the  death  claims  of  the  year,  while  the  balance  thereof  is 
carried  to  reserve  account.  Thus,  for  convenience  sake 
merely,  we  may  designate  one  portion  of  the  year's  net 
premium  as  the  "mortality  element"  and  the  balance  as 
the  "reserve  element,"  but  it  is  nevertheless  apparent, 
that  the  division  as  made  is  in  no  way  fixed.  The  so- 
called  elements  necessarily  vary  in  their  relative  propor- 
tions from  year  to  year,  just  as  the  mortality  of  the 
company  steadily  increases  with  the  age  of  the  members, 
while  the  contribution  from  interest  also  increases  yearly 
as  the  reserve  grows  larger. 

We  have  referred  to  these  errors  at  length,  because 
they  are  still  widely  prevalent  and  constitute  the  basis 
of  most  assessment  fallacies,  making  it  quite  essential 
that  the  solicitor  in  the  beginning  of  his  career  should 
know  how  to  meet  and  refute  them. 

Let  us  state  then,  as  emphatically  as  possible,  that 
the  gross  premium  is  not  composed  of  three  elements, 
"mortality,  reserve  and  expense,"  but  consists  of  two 
parts  only,  the  net  premium  and  the  loading,  and  that 
the  net  premium  is  all  for  mortality  purposes.  As  al- 
ready stated,  you  have  seen  in  your  study  of  the  Verification 
Table,  pages  46  and  47,  that  there  is  but  one  '*  insurance 

65 


fund"  from  which  all  death  claims  are  paid.  This  fund 
consists  of  the  entire  net  premium  receipts  plus  interest 
thereon  at  the  assumed  rate;  and  the  Reserve  is  simply 
the  balance  of  the  fund  on  hand  at  any  given  time. 
That  indeed  is  the  literal  meaning  of  the  term.  That 
portion  of  the  insurance  fund  which  has  been  expended 
has  not  been  reserved.  That  which  remains  is  reserved 
for  the  payment  of  the  claims  of  succeeding  years ;  hence 
its  designation  as  "The  Reserve."  This  balance  is 
increased  yearly  by  the  addition  of  the  current  net 
premium  income  and  interest  at  the  assumed  rate.  It 
is  likewise  constantly  drawn  upon  for  the  payment  of 
claims.  The  balance  on  hand  is  always  the  reserve. 
(Verification  Table,  columns  5  and  8.)  In  short,  there  is 
absolutely  no  distinction  between  mortality  element  and 
reserve  element,  or  between  mortality  fund  and  reserve 
fund,  save  the  distinction  between  money  which  is  ex- 
pended now  and  money  which  is  held  for  future  dis- 
bursement. 

Cash  Values  and  Endowments:  Their  Relation  to 
The  Reserve 

If  a  policy-holder  surrenders  his  contract  and 
withdraws  from  the  copQpany,  the  latter  is  relieved  of 
further  liability  on  account  of  that  policy.  It  will  never 
mature  as  a  death  claim.  It  is  no  longer  necessary, 
therefore,  to  hold  a  reserve  for  that  policy  and  accord- 
ingly the  member  may  be  permitted  to  withdraw  as  a 
Cash  Surrender  Value  a  sum  not  exceeding  his  propor- 
tionate share  of  the  whole  reserve.     If  less  than  the  full 

66 


proportion  of  the  reserve  pertaining  to  the  cancelled  pol- 
icy is  allowed  as  a  surrender  value,  the  remainder  no 
longer  constitutes  a  part  of  the  fund,  but  becomes  sur- 
plus, available  for  subsequent  apportionment  among  the 
remaining  members  as  hereafter  explained.  The  fund 
will  then  stand  the  same  as  if  the  withdrawing  policy- 
holder had  never  been  a  member  of  the  company. 

The  Verification  Table  demonstrates  the  sufficiency 
of  the  ordinary  life  net  premium.  Had  every  member 
of  our  hypothetical  company  carried  an  endowment  policy 
instead  of  an  ordinary  life,  a  similar  computation  would 
have  proved  likewise  the  sufficiency  of  the  endowment 
net  premium.  Indeed,  the  ordinary  life  policy  at  age 
fifty-six  as  illustrated  by  the  Table  might  be  regarded  as 
a  forty-year  endowment,  since  the  reserve  becomes  equal 
to  the  face  of  the  policy  at  the  end  of  forty  years,  at  the 
attained  age  of  ninety-six.  In  reality,  every  life  policy 
is  the  mathematical  equivalent  of  an  endowment  policy 
in  some  form.  This  may  be  illustrated  by  the  inter- 
esting case  of  Charles  H.  Booth,  the  first  policyholder 
to  attain  the  age  of  96.  Mr.  Booth's  policy  was  an 
ordinary  life,  issued  at  age  thirty-nine.  Fifty-seven 
years  later,  therefore,  he  reached  the  assumed  limit  of 
life,  ninety-six  years.  The  reserve  then  became  equal  to 
the  face  of  the  policy,  the  premium  having  been  computed 
upon  the  assumption  that  he  would  not  live  beyond  that 
age  and  that  the  face  amount  would  then  become  payable. 
Had  he  applied  for  a  fifty-seven  year  endowment  at  age 
thirty-nine,  the  face  of  his  policy  would  likewise  have 
become  payable  at  age  ninety-six.  In  either  case  the 
net  premium  would  have  been  precisely  the  same  and  the 


reserve  on  the  two  policies  would  have  been  identical  in 
amount  at  every  stage  during  the  fifty-seven  years.  In 
other  words,  an  ordinary  life  policy  and  a  fifty-seven  year 
endowment,  issued  at  age  thirty-nine,  are  mathematically 
identical.  Likewise  an  ordinary  life  policy  at  fifty-six 
is,  mathematically,  a  forty-year  endowment  issued  at 
the  same  age.  Every  life  policy  is,  mathematically,  an 
endowment  policy  payable  at  age  ninety-six.  There  is 
this  difference,  however,  to  be  noted.  While  the  reserve 
of  a  life  policy  is  equal  to  the  face  amount  at  age  96,  so 
that  the  policy  may  properly  be  paid  in  cash  at  that  time, 
it  is  not,  by  its  terms,  payable  until  death,  which  may  be 
several  years  later.  On  the  other  hand,  a  40  year  endow- 
ment issued  at  age  56  is  by  its  terms  absolutely  payable 
at  96. 

Single  Premiums  and  Reserves 

You  have  seen  on  page  19  that  if  each  of  the 
6S,S64  members  of  our  hypothetical  company  were  to 
pay  for  his  insurance  with  a  single  premium  ($621.18), 
we  should  have  a  total  insurance  fund  of  $39,360,583.39. 
No  further  payments  on  the  part  of  any  member  would 
ever  be  necessary,  since  the  stated  fund,  with  the  help  of 
interest  at  three  per  cent.,  would  be  precisely  sufficient 
for  the  payment  of  all  claims  as  they  mature,  including 
those  of  the  last  three  members  at  age  ninety-six.  In 
other  words,  each  member  would  hold  from  the  start  a  fully 
paid  life  policy  of  $1,000. 


The  following  table  shows  the  net  single  premium 
required  for  a  fully  paid  whole  life  policy  at  every  age 
from  twenty  to  ninety-five: 

Net  Single  Premiums,  or  Reserve  Values  on 
Paid-up  Policies  Per  $1,000 


Present 
Age 

Net  Single 
Premium 

Present 
Age 

Net  Single 
Premium 

Present 
Age 

Net  Single 
Premium 

or  Reserve 

or  Reserve 

or  Reserve 

20 

$330  94 

46 

$514  80 

72 

$796  67 

21 

885  68 

47 

524:23 

73 

806  28 

22 

340  57 

48 

534^37 

74 

815  70 

23 

345  62 

49 

644i70 

75 

824  93 

24 

350  82 

50 

555  22 

76 

834  01 

25 

856  18 

51 

565  89 

77 

842  97 

26 

861  72 

52 

576  71 

78 

851  80 

27 

367  43 

53 

587  67 

79 

860  49 

28 

373  32 

54 

598  74 

80 

869  06 

29 

379  39 

55 

609  92 

81 

877  42 

30 

386  64 

56 

621  18 

82 

885  60 

81 

892  09 

57 

•  632  51 

83 

893  63 

32 

398  73 

58 

643  89 

84 

901  59 

83 

405  58 

59 

655  30 

85 

909  51 

34 

412  63 

60 

666  72 

86 

917  32 

35 

419  88 

61 

678  13 

87 

924  88 

86 

427  88 

62 

689  51 

88 

982  02 

37 

435  04 

63 

700  83 

89 

938  75 

38 

442  95 

64 

712  08 

90 

945  23 

89 

451  07 

65 

723  24 

91 

951  58 

40 

459  42 

66 

734  27 

92 

957  49 

41 

468  00 

67 

745  16 

93 

962  31 

42 

476  80 

68 

755  89 

94 

966  84 

43 

485  83 

69 

766  42 

95 

970  87 

44 

495  10 

70 

776  73 

45 

504  59 

71 

786  82 

If  any  large  number  of  persons,  say  100,000,  all 
of  the  age  of  twenty  years,  were  each  to  contribute 
toward  a  common  insurance  fund  the  net  single  premium 
of  $330.94,  the  total  resulting  fund  of  $33,094,000 
would  be  just  sufficient  with  three  per  cent,  interest  for 
the   payment  of  all  outstanding  policies   as   the  same 

60 


mature  according  to  the  mortality  table.  Likewise  at 
age  fifty  the  net  single  premium  required  to  accomplish 
this  result  would  be  $555.22.  At  ninety-five  the  net 
premium  required  is  $970.87.  If  to  that  sum  we  add 
one  year's  interest  at  three  per  cent.  ($29.13),  we  shall 
have  at  the  end  of  the  year  $1,000,  or  just  enough  to 
pay  the  member  in  full  at  his  then  age  of  ninety-six. 

But  the  total  insurance  fund  on  hand  is  always 
the  reserve,  and,  dividing  that  fund  by  the  number  of 
living  members,  we  obtain  the  reserve  pertaining  to  each 
policy.  One  thousand  members  at  age  fifty,  contributing 
each  a  net  single  premium  of  $555.22,  create  a  total 
insurance  fund  of  $555,220;  and  dividing  that  fund 
again  by  the  number  of  members,  we  obtain  necessarily 
the  sum  of  $555.22  as  the  reserve  on  each  paid-up  policy. 
In  other  words,  the  net  single  premium  at  a  given  age 
is  always  the  reserve  on  a  paid-up  policy  at  that  age. 

To  illustrate:  Turn  to  the  schedule  of  reserve 
values  in  your  Life  Insurance  Manual  or  Handy  Guide. 
Take  the  case  of  a  fifteen-payment  life  policy  issued  at 
age  twenty-five.  It  becomes  paid-up  at  age  forty. 
Note  that  the  accumulated  reserve  then  amounts  to 
$459.42,  corresponding  to  the  net  single  premium  at 
that  age  as  given  in  the  above  table.  Or  take  a  life 
policy  issued  at  age  thirty  and  paid  for  in  ten  equal 
annual  premiums.  This  also  becomes  fully  paid-up  at 
age  forty,  and  again  you  find  the  reserve  at  that  age  to 
be  $459.42.  In  short,  for  "Net  Single  Premiums"  in 
the  foregoing  table,  you  may  read  "Reserve  Values  of 
Paid-up  Policies,"  for  the  two  terms  are  precisely 
equivalent. 

eo 


The  Reserve  Not  the  Property  op  the 
Individual  Policy-Holder 

It  is  scarcely  necessary  to  point  out  that  while  the 
reserve  on  a  paid-up  policy  at  age  fifty-six  is  $621.18, 
the  reserve  on  the  same  policy  one  year  later,  at  age 
fifty-seven,  will  be  $632.51,  and  ten  years  later,  at  age 
sixty-six,  will  be  $734.27,  as  shown  in  the  foregoing 
table,  page  59.  This  enables  us  to  correct  another  very 
common  misconception  as  to  the  nature  of  the  reserve. 

The  beginner  often  conceives  the  idea  that  the 
reserve  is  a  distinct  fund  belonging  to  each  policy — a 
fund  which  goes  on  accumulating  at  three  per  cent, 
interest  until  the  death  of  the  insured,  when  it  is 
applied  in  part  payment  of  his  policy ;  or,  if  he  continues 
to  live,  accumulating  until  he  reaches  the  age  of  ninety- 
six  years,  when  it  amounts  to  the  face  of  the  policy. 
This  view  of  the  reserve  is  essentially  erroneous.  Take 
for  instance  the  reserve  of  a  paid-up  policy  at  age  fifty- 
six,  to  wit:  $621.18.  Add  three  per  cent,  interest  ($18.64) 
and  you  obtain  $639.82,  while  the  actual  reserve  one 
year  later  as  shown  by  the  table  (see  age  fifty-seven), 
is  only  $632.51.  In  like  manner,  compounding  the 
interest  for  ten  years  on  $621.18,  the  reserve  at  fifty-six, 
you  will  obtain  a  much  larger  sum  than  $734.27,  the 
reserve  at  age  sixty-six;  while  on  the  same  basis  the 
reserve  of  $621.18  at  age  fifty-six  would  amount  to 
$1,000  long  before  reaching  the  age  of  ninety-six. 

The  error  consists  in  assuming  that  the  reserve  is 
a  distinct  fund  specifically  belonging  to  each  policy  and 
never  drawn  upon  until  applied  as  part  payment  of  that 

61 


policy  at  death.  In  life  insurance  the  reserve  is  the 
common  insurance  fund  belonging  to  the  whole  body  of 
policy-holders, — not  their  property  as  individuals,  but  as 
a  company.  It  does  accumulate  at  three  per  cent, 
interest,  but  is  constantly  drawn  upon,  both  principal 
and  interest,  for  the  payment  of  claims.  For  many 
purposes  it  may  at  any  time  become  desirable  to  ascertain 
the  pro  rata  portion  of  the  reserve  on  hand  pertaining  to 
each  policy  in  force,  as  we  have  done  in  this  discussion, 
but  this  does  not  mean  that  the  ascertained  pro  rata 
reserve  is  in  any  case  a  distinct  fund  actually  belonging 
to  that  policy,  or  to  the  holder  thereof  as  an  individual 
Neither  can  the  terminal  reserve,  even  in  the  case  of  a 
paid-up  policy,  be  determined  by  adding  three  per  cent, 
to  the  reserve  of  the  preceding  year  for  the  reason  that 
the  fund  is  constantly  drawn  upon  to  meet  the  demands 
of  the  current  mortality.  At  age  ninety-five,  and  at  that 
age  only,  this  process  will  give  the  correct  result,  because 
the  limit  of  life  is  reached  at  ninety-six. 

Reserve  Tables 

In  the  Verification  Table  (column  9),  is  shown  the 
pro  rata  terminal  reserve  for  each  year  in  the  case  of  an 
ordinary  life  policy  issued  at  age  fifty-six.  Tables  have 
been  constructed  showing  the  pro  rata  reserve  at  the 
middle  and  end  of  every  policy  year,  corresponding  to 
various  forms  of  policies  issued  at  any  age.  The  initial 
reserve,  which  is  the  reserve  at  the  beginning  of  a  policy 
year,  is  found  by  adding  the  terminal  reserve  of  the 
preceding  year  to  the  net  premium.  The  balance  on 
hand  at  the  middle  of  the  policy  year  is  termed  the 


Mean  Reserve,     It  is,  of  course,  one-half  of  the  sum  of 
the  initial  and  terminal  reserves  of  that  year. 

Rapid  Accumulation  of  Reserves 

Referring  again  to  the  Verification  Table,  observe 
that,  although  no  new  insurance  is  written  by  our 
hypothetical  company,  the  total  reserve  rapidly  increases 
until  the  end  of  the  fourteenth  year,  when  it  amounts  to 
$15,837,373.42.  From  that  time  on  the  aggregate 
amount  decreases  yearly  because  of  the  greater  drain 
resulting  from  an  increasing  death  rate. 

Uninformed  people  are  prone  to  conclude,  on  per- 
ceiving how  greatly  the  premium  receipts  in  the  earlier 
years  exceed  the  death  claims,  that  we  are  collecting 
more  money  than  necessary,  and  that  the  net  premium  is 
larger  than  need  be.  Advocates  of  assessmentism  and  of 
other  unscientific  forms  of  life  insurance  constantly  urge 
this  view;  but  to  perceive  the  fallacy  involved  we  have 
only  to  glance  down  the  table  to  age  sixty-eight,  in  the 
thirteenth  year,  to  find  the  death  claims  already  exceed- 
ing the  premium  receipts;  while  twelve  years  later,  at 
age  eighty,  the  yearly  mortality  is  over  three  times  the 
premium  income. 

Uninformed  persons  also  complain  of  the  enormous 
reserves  piled  up  by  life  insurance  companies,  not  know- 
ing that  the  accumulation  is  merely  the  result  of  a  low 
mortality  in  the  earlier  years,  thus  leaving  a  large  balance 
on  hand  at  the  end  of  each  year,  every  dollar  of  which, 
however,  will  be  needed  to  meet  the  much  higher  mor- 
tality of  later  years.  If  the  death  rate  were  uniform 
through  life,  the  same  number  per  thousand  dying  at  age 


twenty  as  at  age  eighty — the  premium,  which  would  be 
the  same  for  all  ages,  would  be  precisely  sufficient  for  the 
payment  of  current  death  claims,  leaving  no  balance  at 
the  end  of  the  year,  and  no  large  accumulation  would  be 
necessary. 

The  reader  will  readily  perceive  that  if  new  mem- 
bers in  large  numbers  were  added  to  our  hypothetical 
company  each  year,  the  aggregate  reserve  would  increase 
still  more  rapidly,  and  if  the  yearly  additions  to  the 
membership  were  steadily  maintained  at  a  uniform  rate, 
it  would  necessarily  be  many  years  before  the  accumula- 
tion of  funds  would  become  stationary;  yet  every  doUar 
of  this  reserve  would  be  needed  ultimately  for  mortality 
purposes,  being  merely  the  balance  on  hand  of  the  insur- 
ance fund  mathematically  necessary  for  the  final  payment 
of  outstanding  policies. 

The  Meaning  op  Large  Reserves. 

As  an  illustration  of  the  rapid  accumulation  of  the 
reserve  in  actual  practice,  that  of  The  Mutual  Life 
Insurance  Company  of  New  York,  which  amounted  to 
$366,620,552.73  on  the  31st  of  December,  1904,  had  in- 
creased ten  years  later,  on  December  31,  1914,  to  the 
sum  of  $496,438,884,  not  including  the  Company's 
contingency  reserve,  reserve  for  supplementary  contracts, 
and  accumulations  for  deferred  dividends  of  over  seventy 
millions  more.  This  increase  has  been  merely  com- 
mensurate with  the  rapid  growth  and  increasing 
obligations  of  the  Company,  and  the  fund  is  no  greater 
than  it  was  ten  years  ago  in  proportion  to  the  require- 
ments of  existing  policy  contracts.  Likewise  our  "hypo- 
thetical company"  (see  Verification  Table,  pages  46  and 

M 


47)  is  no  stronger  at  the  end  of  eight  years  with  a  reserve  of 
$12,292,773.41,  or  at  the  end  of  fourteen  years  with  a 
reserve  of  $15,837,373.42,  than  at  the  end  of  its  first 
year,  with  only  $1,857,110.99;  since  in  each  case  the 
balance  on  hand  is  merely  the  amount  which  is  mathe- 
matically necessary,  in  connection  with  future  premiums 
called  for  by  existing  policies,  for  the  ultimate  payment 
of  those  policies.  For  the  same  reason  the  company 
is  no  stronger  at  the  end  of  thirty-five  years,  when  the 
pro  rata  reserve  pertaining  to  each  policy  is  $872.18, 
than  at  the  end  of  its  first  year  when  it  is  only  $29.90. 

The  amount  of  the  reserve  at  any  given  time 
depends  also  upon  the  nature  of  the  business  written. 
Were  the  members  of  our  hypothetical  company  each 
insured  under  a  thirty-year  endowment  contract,  the 
necessary  reserve  or  insurance  fund  at  the  end  of  the 
thirtieth  year  would  be  $4,193,000  instead  of  $3,277,- 
749.20,  since  the  policies  of  the  4,193  members  still 
living  would  all  be  payable  in  full  at  that  time.  In 
endowment  insurance  the  reserve  necessarily  equals  the 
face  of  the  policy  at  the  end  of  the  endowment  period, 
and  (if  the  endowment  is  payable  before  age  96),  is 
correspondingly  larger  in  each  preceding  year  than  the 
reserve  of  a  life  policy.  The  reader  will  perceive  the 
absurdity  of  exploiting  the  ratio  of  "Accumulated 
Reserves  to  Mean  Insurance  in  Force,"  sometimes 
resorted  to  in  compai^ng  one  regular  life  insurance 
company  with  another,  the  company  with  the  larger 
reserves  per  $1,000  of  outstanding  insurance  (both  being 
on  the  same  reserve  basis),  absurdly  claiming  to  be  the 
stronger  institution. 

65 


CHAPTER  VII 

The  Amount  at  Risk 

\\T  HEN  a  life  insurance  policy  matures  as  a  death 
claim,  the  difference  between  the  face  of  the  policy 
and  the  terminal  reserve  may  be  regarded  as  the  net  loss 
to  the  company,  for  the  reason  that  the  pro  rata  reserve 
of  the  policy  represents  the  amount  of  that  policy's  con- 
tribution to  the  insurance  fund  which  still  remains  on 
hand.  In  other  words,  the  pro  rata  reserve  of  the  policy 
may  be  regarded  as  the  amount  which  it  contributes 
towards  its  own  payment.  The  difference  between  the 
face  amount  of  the  policy  and  the  reserve  is  therefore 
called  the  Amount  at  Risk,  and  the  reserve  itself  has 
been  termed  Self  Insurance. 

These  are  technical  terms,  useful  in  the  statement 
of  certain  propositions,  but  not  to  be  understood  in  their 
literal  sense.  Strictly  speaking,  the  maturing  of  a  policy 
by  death  can  not  be  regarded  as  a  loss  to  the  company, 
either  in  whole  or  in  part,  provided  the  mortality  of 
the  company  is  not  in  excess  of  that  indicated  by  the 
table  upon  which  its  rates  are  based.  (See  page  34). 
It  is  the  business  of  a  life  insurance  company  to  pay 
death  claims,  and  the  entire  cost  of  the  payment^ 
whether  the  particular  policy  has  been  in  existence  for 
a  day  or  a  year  or  for  many  years,  has  been  provided  for 
in  the  premium  rates.  The  payment  of  a  death  claim  is  no 
more  a  loss  to  the  company  than  is  the  payments  of  its 
ordinary  expenses,  full  provision  for  the  one  item  having 
been  made  in  the  reserve  or  insurance  fund,  for  the  other 
in  the  loading. 


An  endowment  policy  maturing  by  completion 
of  the  endowment  period  is  technically  and  literally  a 
Claim,  not  a  Loss,  On  the  other  hand,  a  policy  maturing 
by  the  death  of  the  insured  may  be  technically  termed  a 
Loss,  but  is  literally  a  Death  Claim,  It  is  a  claim  for 
its  face  amount,  and  the  face  of  the  policy  is  literally, 
though  not  technically,  the  amount  at  risk.  The  latter 
term  is  in  general  use,  and  its  technical  signification  is 
fully  established  and  must  be  kept  in  mind.  The  use  of 
the  term  will  be  clearly  illustrated  by  the  following  table, 
based  on  the  figures  of  our  hypothetical  company.  (See 
Verification  Table,  pages  46  and  47.) 


Age 

No.  of 

Face  of 

Terminal 

Amount 

No.  of 

End 

of 
Year 

Members 

Policy 

Reserve 

at  Risk 

Deaths 

56 

63,364 

$1,000  00 

$29  90 

$970  10 

1,260 

1 

60 

57,917 

1,000  00 

150  33 

849  67 

1,546 

5 

70 

38,569 

1,000  00 

437  25 

562  75 

2,391 

15 

80 

14,474 

1,000  00 

676  42 

323  58 

2,091 

25 

85 

5,485 

1,000  00 

78173 

218  27 

1,292 

30 

90 

847 

1,000  00 

87218 

127  82 

385 

35 

95 

3 

1,000  00 

1,000  00 

000 

3 

40 

Cost  or  Insurance 
Taking  the  amount  at  risk  in  its  technical  sense  as 
the  actual  loss  in  the  case  of  a  death  claim,  we  determine 
the  mortality  cost,  or  Cost  of  Insurance,  for  the  year  as 
follows.  At  age  fifty-six  the  amount  at  risk  on  an  ordinary 
life  policy  in  the  first  year  is  $970.10.  Of  the  63,364! 
members  comprising  our  hypothetical  company,  1,260 
will  die  during  the  year,  making  the  net  loss  $970.10 
multiplied  by  1,260  or  $1,222,326.00,  which  is  the  total 
cost  of  insurance  for  the  year.  Dividing  this  amount  by 
63,364,  the  number  living  at  the  beginning  of  the  year, 
we  obtain  $19.29,  which  is  the  pro  rata  cost  of  Insurance 

67 


per  $1,000  for  the  first  year.  In  the  fifth  year  the 
amount  at  risk  is  $849.67,  and  multiplying  this  by  1,546, 
the  tabularnumber  of  deaths,  we  get  $1,313,589.82  as  the 
total  cost  of  insurance  for  the  year.  Dividing  by  57,917, 
the  number  living  at  the  beginning  of  the  year,  we  obtain 
$22.68  as  the  cost  of  insurance  per  $1,000  in  the  fifth 
year.  At  ninety  the  amount  at  risk  is  $127.82  and  the 
total  cost  of  insurance  is  that  sum  multiplied  by  385,  or 
$49,210.70.  Dividing  by  847,  the  number  living  at  the 
beginning  of  the  year,  we  obtain  $58.10  as  the  cost  of 
insurance  per  $1,000  in  the  thirty-fifth  year. 

Mortality 

The  death  rate  per  1,000  lives  as  indicated  by 
the  mortality  table  is  termed  the  Tabular  Mortality. 
If  the  lives  insured  have  been  well  selected,  the  Actual 
Mortality  will  probably  be  less  than  the  tabular,  or  that 
which  was  expected  according  to  the  table.  If  in  the 
fifth  year  of  our  hypothetical  company,  for  instance,  the 
number  of  deaths  should  be  only  1,500  instead  of  1,546, 
the  actual  cost  of  mortality  would  be  the  amount  at  risk, 
$849.67,  multiplied  by  1,500,  the  actual  number  of 
deaths,  or  $1,274,505.    In  that  case  we  should  have: 

Total  cost  of  Insurance,  or 
Expected  Mortality     -     -     $1,313,589.82 
Actual  Mortality     -     -     -       1,274,505.00 
Saving  in  Mortality     -     -  $39,084.82 

In  legitimate  life  insurance  the  ratio  or  per- 
centage of  "Death  Claims  Incurred  to  Mean  Amount  of 
Insurance  in  Force,"  so  often  exploited  in  competitive 
literature,  is  of  no  significance  whatever  since  it  ignores 


two  essential  factors — the  ages  of  the  insured  and  the 
amount  of  reserves  accumulated.  Likewise  the  ratio  of 
the  "Face  Amount  of  Death  Claims  Incurred  to  the  Face 
Amount  of  Expected  Death  Claims"  is  misleading,  for 
the  reason  that  again  the  accumulated  reserves  are  ig- 
nored. Only  by  comparing  the  total  amount  at  risk  on 
accruing  claims  (actual  mortality)  with  the  total  amount 
at  risk  on  expected  claims  as  indicated  by  the  mortality 
table  (**  cost  of  insurance  "  or  expected  mortality) ,  can  we 
determine  whether  or  not  there  has  been  a  Saving  in 
Mortaliiy. 

To  illustrate:  Our  hypothetical  company  has  at 
the  beginning  63,364  members  at  age  fifty-six,  with 
$63,364,000  insurance  in  force.  (See  Verification  Table, 
pages  46  and  47,  also  Amount  at  Risk,  page  QQ).  Twelve 
hundred  and  sixty  members,  according  to  the  table,  are 
dead  at  the  end  of  the  year,  making  total  death  claims 
$1,260,000.  Dividing  we  obtain  the  ratio  of  "Death 
Claims  to  Insurance  in  Force,"  to  wit:  $19.88  per  $1,000, 
or  practically  twenty  deaths  per  thousand  members. 
($1,260,000  :63,364=$19.88.)  In  the  same  way  the 
"insurance  in  force"  during  the  fifteenth  year,  when 
our  members  have  attained  the  age  of  seventy  years, 
is  $38,569,000,  the  death  claims  $2,391,000,  and  the 
mortality  per  $1,000  is  $61.99,  or  nearly  sixty-two 
deaths  per  thousand  members.  In  this  instance  the 
apparent  mortality,  or  the  ratio  of  death  claims  to  insur- 
ance in  force,  is  over  three  times  that  at  age  fifty-six; 
and  yet  in  either  case  we  have  only  the  normal  mortality, 
or  precisely  what  we  counted  on  and  provided  for  in  the 
computation  of  the  premium. 


The  apparently  high  death  rate  at  seventy  does 
not  affect  the  financial  condition  of  our  hypothetical 
company,  conducted  as  it  is  on  a  plan  which  is  mathe- 
matically correct.  In  fact,  without  increasing  premium 
rates  in  the  least,  it  is  precisely  as  easy,  because  of  the 
accumulated  reserves,  to  meet  the  mortality  of  $61.99 
per  $1,000  at  age  seventy  as  that  of  $19.88  at  age  fifty- 
six.  Indeed,  notwithstanding  the  death  claims  at  seventy 
are  largely  in  excess  of  the  premium  income — in  excess, 
in  fact,  of  total  income — the  reserve  pertaining  to  each 
policy  in  force  at  the  end  of  the  year  has  grown  to 
$437.25,  an  increase  of  $26.63  over  that  of  the  previous 
year  (see  Verification  Table,  pages  46  and  47).  In  the 
same  way  at  age  eighty-five,  with  $235.55  of  death  claims 
per  $1,000  of  insurance  in  force,  and  with  total  death 
claims  amounting  to  nearly  five  times  the  premium  income 
and  to  over  three  times  the  total  income,  the  mortality  is 
promptly  met,  while  the  individual  reserve  increases  as 
before  from  $761.12  to  $781.73.  That  is  to  say,  in  legiti- 
mate life  insurance,  so  long  as  the  actual  mortality  does 
not  exceed  the  expected,  it  is  immaterial  whether  the  ratio 
of  death  claims  to  mean  insurance  in  force  is  $19.88,  or 
$61.99,  or  $235.55  per  $1,000;  i.  e.,  whether  the  death 
rate  is  20,  or  62,  or  236  per  1,000  members.  The  mor- 
tality is  precisely  what  was  expected  and  what  has  been 
provided  for,  and  is  as  easily  met  in  the  one  case  as  in 
the  other. 

On  the  other  hand,  in  assessment  life  insurance 
a  death  rate  in  excess  of  ten  per  1,000,  or  a  mortality 
of  more  than  ten  dollars  per  $1,000  insurance  in  force, 
is  significant;  for  it  means  increasing  assessments  and 

70 


cost,  with  the  inevitable  result  of  a  decreasing  member- 
ship and  ultimate  dissolution.  The  relatively  small 
emergency  funds  of  the  assessment  society  are  insufficient 
to  meet  the  increasing  death  claims  pertaining  to  the 
increasing  ages  of  the  several  members.  In  legitimate 
life  insurance  the  reserve  pertaining  to  each  policy 
increases  proportionately  with  the  advancing  age  of  the 
policy-holder,  and  the  ratio  of  Actual  to  Expected 
Mortality,  which  takes  into  account  these  accumulating 
reserves,  is  alone  of  any  significance. 

The  Average  Age 

In  100,000  persons  all  of  the  age  of  thirty-five 
years,  the  tabular  or  expected  deaths  according  to  the 
American  Experience  Table  (see  page  13)  will  be  895, 
a  mortality  rate  of  8.95  per  thousand.  In  the  same 
number  of  persons  of  various  ages  but  with  an  average 
age  of  thirty-five,  the  tabular  or  expected  mortality  may 
or  may  not  be  8.95  per  thousand.  It  depends  upon  the 
relative  proportions  of  young  and  aged  members,  not 
upon  the  average  age.  For  example:  In  50,000  persons 
all  of  the  age  of  twenty  years,  the  tabular  number  of 
deaths  will  be  S90.  In  the  same  number  of  lives  at  age 
fifty  the  tabular  deaths  will  be  689.  The  average  age 
of  the  100,000  persons  will  be  thirty-five,  but  the  total 
deaths  according  to  the  mortality  table  will  be  1,079, 
(390  +  689),  a  death  rate  of  10.79  per  thousand.  Thus 
it  is  apparent  that  the  average  age  of  a  body  of  men 
is  of  little  significance.  The  normal  or  tabular  death 
rate  at  age  thirty-five  is  8.95,  but  in  a  body  of  men 

71 


whose  average  age  is  thirty-five,  an  actual  mortality 
of  10.79  or  more  may  or  may  not  be  excessive.  All 
depends  upon  the  several  ages  of  the  individual  members. 
Nothing  can  be  predicated  upon  the  average  age. 

Probability  of  Dying 

At  age  fifty-six,  of  63,364  persons,  1,260  will  be 
dead  at  the  end  of  one  year  according  to  the  American 
Experience  Table  of  Mortality.  The  Probability  of  Dying 
within  the  year,  therefore,  will  be  represented  by  the 
fraction  -g^?^^ .  This  fraction  is  equivalent  to  the  decimal 
.019885,  which  means  a  death  rate  of  19.88  per  1,000. 
Of  the  same  body  of  men  there  will  be  62,104  still  living 
at  the  end  of  the  year,  so  that  the  Probability  of  Living 
through  the  year  will  be  ff.'irij  equivalent  to  the  decimal 
.980115.  Observe  that  the  sum  of  the  two  decimals  is 
unity,  the  probability  of  living  being  the  complement  of 
the  probability  of  dying. 

Again,  of  63,S64s  persons  living  at  age  fifty-six, 
2,585  will  be  dead  at  the  end  of  two  years,  the  proba- 
bility of  dying  within  that  period  being  -o.Wf*  or 
.040796,  while  the  probability  of  living  beyond  that 
period  is  K.ifl,    or  .959204. 

The  Expectation  of  Life 
The  Expectation  of  Life  is  the  average  length  of 
time  that  a  number  of  persons  of  a  given  age  will  live 
according  to  the  specified  table  of  mortality.  Thus, 
taking  the  case  of  our  hypothetical  company,  it  is 
assumed  by  the  American  Experience  Table  (Page  13), 
that  of  the  63,364  persons  living  at  age  fifty-six,  three 
will  live  thirty-nine  complete  years,  to  age  95 — ^the  last 

72 


one  of  the  three  not  beyond  age  96, — eighteen  will  live 
thirty-eight  full  years,  2,091,  twenty-four  full  years, 
1,980,  nine  full  years,  1,260,  less  than  one  full  year,  etc., 
and  that  the  whole  body  will  live  for  an  average  time  of 
16.72  years,  which  is  accordingly  the  expectation  of  life 
at  age  fifty-six.  A  better  term  than  "expectation  of 
life"  is  that  of  Average  Future  Lifetime,  or  Average 
After-Lifetime. 

The  expectation  of  life  at  a  given  age  does  not 
mean  that  one-half  of  all  persons  living  at  that  age  will 
die  in  that  time.  For  example:  At  forty-three,  the 
expectation  of  life  is  twenty-six  years,  but  it  does  not 
follow  that  half  the  persons  now  living  at  age  forty-three 
will  die  within  the  next  twenty-six  years.  On  the  con- 
trary, by  reference  to  the  mortality  table  (Page  IS)  it 
will  be  seen  that  of  75,782  persons  living  at  forty-three, 
40,890,  or  considerably  more  than  half,  will  still  be  living 
twenty-six  years  later  at  age  sixty-nine.  One-half  of  the 
original  number,  37,891,  according  to  the  Table,  will  die 
within  twenty-seven  years,  three  months  and  twelve  days. 
This  period — the  length  of  time  during  which  one-half 
of  the  persons  of  a  given  age  will  continue  to  live— is 
technically  termed  the  Probable  Life — ^the  French  term, 
Vie  Probable,  being  commonly  used.  The  term  is  not 
a  satisfactory  one,  since  there  is  in  every  case  a  definite 
probability,  according  to  the  Table,  of  living  to  any  age 
up  to  ninety-six,  the  degree  of  probability  varying  accord- 
ing to  the  length  of  the  period  under  consideration.  In  as 
much  as  40,890  of  75,782  persons  living  at  age  forty- 
three  will  still  be  living  at  age  sixty-nine  according  to 
the  table,  the  probability  at  the  former  age  of  living  to 

78 


sixty-nine,  will  be  expressed  by  the  fraction  TT.ilf  > 
while  the  probability  of  living  fifty  years,  or  to  age 
ninety-three,  will  be  expressed  by  tt?A^j  o^  .001042, 
since  out  of  75,782  persons  at  forty-three,  seventy-nine 
will  still  be  living  at  ninety-three. 

The  foregoing  observations  sufficiently  illustrate 
the  fallacy  involved  in  the  notion  entertained  by  the 
advocates  of  assessment  insurance  that  the  expectation  of 
life  has  any  relation  to  the  cost  of  life  insurance.  It  is  an 
error  to  suppose  that  a  man  who  bids  fair  to  live  through 
his  expectation  of  life  is  for  that  reason  a  good  risk,  or 
that  the  man  who  has  paid  his  premiums  for  that  length 
of  time  has  paid  the  full  cost  of  his  insurance.  If  every 
member  of  our  hypothetical  company  still  living  at  the 
end  of  seventeen  years — his  expectation  of  life — were 
then  to  be  relieved  of  paying  further  premiums,  the  total 
receipts  from  that  source  would  be  reduced  by  several 
millions  (see  Verification  Table,  pages  46  and  47),  and 
the  net  premium  of  $47-76  would  have  to  be  materially 
increased. 

The  distinction  should  be  made  between  the 
probability  of  dying  within  a  certain  number  of  years, 
and  the  probability  of  dying  in  a  particular  year.  At 
forty-three,  the  chances  of  dying  within  twenty-seven 
years,  three  months  and  twelve  days,  or  of  living  beyond 
that  period,  are  even;  but,  while  a  man  of  forty-three  is 
more  likely  to  live  to  sixty-nine  than  to  seventy-five,  he 
is  at  the  same  time  more  likely  to  die  at  seventy-five 
than  at  the  particular  age  of  sixty-nine,  since  out  of 
75,782  living  at  forty-three,  2,476  will  die  at  seventy- 
five,  against  2,321  at  sixty-nine.  Again  at  age  thirty-five 
the  expectation  of  life  is  31.78  years,  but  the  probability 

74 


of  dying  in  the  thirty-second  year  thereafter,  at  age 
sixty-six,  is  not  so  great  as  that  of  dying  in  the  thirty- 
third,  or  in  the  fortieth,  or  even  in  the  forty-fifth  year. 

Expectation  of  Life  Not  Used  in  Computing  Cost 
OF  Life  Insurance 

The  expectation  of  life  cannot  be  used  in  com- 
puting the  premium  for  the  reason  that  the  computation 
of  compound  interest  as  involved  in  the  cost  of  life  insur- 
ance is  impossible  on  the  basis  of  the  average  after-life- 
time. Compound  interest  is  an  essential  factor  in  the 
computation  of  the  premium,  but,  for  the  reason  stated, 
the  calculation  must  be  made  from  year  to  year  instead 
of  upon  the  basis  of  the  average  time  involved.  The 
theory  that  the  expectation  of  life  may  be  used  as  a  basis 
for  computing  the  probable  cost  of  life  insurance,  is  one 
of  the  widespread  errors  of  assessmentism,  which  the 
intelligent  life  agent  should  be  prepared  to  refute. 


75 


CHAPTER  VIII 

The  Loading 

T  TP  to  this  point  we  have  dealt  with  the  net  premium 
^^  only,  the  whole  of  which  is  calculated  for  mortality 
purposes.  As  a  provision  for  expenses  and  other 
contingencies,  a  specified  sum  called  the  Loading  is 
added  to  the  net  premium,  the  two  combined  making  up 
the  gross  premium  as  given  in  the  rate  book. 

The  Loading  is  sometimes  a  percentage  of  the  net 
premium;  in  other  cases  it  is  composed  of  two  parts — a 
constant  sum  (as  $2.00  per  $1,000  of  insurance  the 
same  at  all  ages),  and  a  percentage  of  the  net  premium; 
while  various  other  methods  are  employed,  the  plan  vary- 
ing with  different  companies,  and  often  with  different 
forms  of  policies  in  the  same  company. 

On  the  theory  that  it  costs  no  more  to  care  for  a 
policy  issued  to  a  member  sixty  years  of  age,  than  for 
one  issued  at  age  forty  or  twenty,  the  claim  is  sometimes 
made  by  the  advocates  of  assessmentism,  that  the  loading 
should  be  a  constant  sum  at  all  ages,  instead  of  being,  in 
whole  or  in  part,  a  percentage  of  the  net  premium.  This 
position  rests  upon  a  false  premise — that  the  loading  is 
for  expenses  only.  The  theory  is  also  untenable  on  other 
grounds. 

The  loading  is  not  for  expenses  only,  but  is  in- 
tended to  provide  for  all  other  possible  contingencies, 
such,  for  instance,  as  a  mortality  in  excess  of  the  tabular 
rate,  interest  earned  less  than  the  assumed  rate,  deprecia- 
tion in  the  values  of  securities,  loss  of  invested  funds,  etc. 

76 


While  the  assumptions  as  to  interest,  mortality,  etc.,  in 
the  computation  of  the  premium,  have  been  on  the  most 
conservative  basis,  nevertheless,  so  long  as  human  judg- 
ment is  fallible,  the  possibility  of  error  must  be  conceded. 
The  foundation  principle  of  life  insurance  is  safety,  and 
if  mistakes  are  to  be  made  at  all,  they  must  be  made  on 
the  side  of  safety.  It  is  better  to  collect  too  much 
money  than  too  little;  hence  the  importance  of  making 
provision  for  unforeseen  contingencies.  But  mortality, 
interest,  investments,  etc.,  all  affect  the  cost  of  life  insur- 
ance; wherefore,  that  part  of  the  loading  which  is 
designed  to  cover  possible  excessive  mortality,  deficit  in 
interest  earnings,  etc.,  has  a  direct  relation  to  the  cost  of 
the  insurance,  and,  like  the  net  premium,  must  vary  with 
the  age  of  the  insured.  This  is  accomplished  by  making 
it  a  percentage  of  the  net  premium. 

Neither  is  it  true  that  the  expense  incident  to  a 
policy  issued  at  sixty  is  no  more  than  that  pertaining  to 
a  policy  issued  at  forty  or  twenty.  The  chief  item  of 
expense  with  any  company  is  that  of  commissions,  and 
this  is  almost  universally  a  percentage  of  the  premium; 
wherefore  the  "loading"  to  provide  for  that  expense  must 
be  greater  at  sixty  than  at  forty  or  twenty.  Taxes  levied 
by  the  various  states  are  an  important  part  of  a  com- 
pany's expenses,  and  these  also  are  almost  always  a  per- 
centage of  the  premium  income. 

It  is  the  common  practice  of  assessment  people  to 
refer  to  the  loading  as  exclusively  an  appropriation  for 
expenses,  charging  directly  that  it  is  all  applied  to  that 
end.  In  refutation  of  this  charge  the  agent  will  explain 
the  true  office  of  the  loading  as  set  out  above,  and  will 

77 


also  point  out  the  fact,  that  so  much  thereof  as  may  not 
be  required  for  the  purpose  designated  is  subsequently 
returned  to  the  policy-holder  when  a  division  of  savings 
is  made.  For  example:  Of  the  loadings  collected  by 
The  Mutual  Life  Insurance  Company  in  1914,  there 
remained  at  the  end  of  the  year  an  unexpended  balance 
of  no  less  than  $2,770,722.42  available  for  return  to 
policy-holders. 

To  Ascertain  the  Loading 

The  amount  of  the  loading  can  be  ascertained  by 
taking  the  difference  between  the  net  and  gross  premiums. 
Tables  of  net  premiums  and  reserves  for  various  forms  of 
policies  at  the  several  ages  and  on  different  reserve  bases 
are  published  in  convenient  form  for  reference.  For 
example:  The  net  premium  of  an  ordinary  life  policy  of 
$1,000,  issued  at  age  thirty-five,  American  Experience 
Table  and  three  per  cent,  interest,  is  $21.08.  If  the 
gross  premium  for  such  a  policy  is  $28.11,  the  difference, 
$7.03,  will  be  the  loading. 

The  net  premium  of  a  particular  policy,  however, 
cannot  always  be  ascertained  from  the  published  tables, 
since  the  amount  depends  upon  the  guarantees  contained 
in  the  contract.  To  illustrate:  On  an  ordinary  life 
policy  of  the  usual  form  but  on  a  three  and  a  half  per 
cent,  reserve  basis,  the  net  annual  premium  at  age  thirty- 
five  is  $19.91,  and  the  regular  reserve  at  the  end  of 
twenty  years  will  be  $310.75.  On  such  a  policy,  how- 
ever, as  issued  in  the  past  by  The  Mutual  Life,  with  a 
twenty-year  distribution  period  and  a  gross  premium  of 
'.88,  the  company  guarantees  a  cash  surrender  value 

78 


at  the  end  of  twenty  years  of  $389.00,  which  necessarily 
requires  a  larger  net  annual  premium  than  $19.91. 

The  Cash  Value,  or  Cash  Surrender  Value  of  a 
policy  is  the  amount  which  the  company  will  pay  to  the 
withdrawing  policy-holder  in  cash  for  the  surrender  and 
cancellation  of  his  contract.  It  is  usually  a  large  fraction 
of  the  reserve  pertaining  to  the  policy,  rarely  the  full 
reserve  until  after  some  years.  Inasmuch  as,  theoreti- 
cally, only  the  good  risk  will  surrender  his  policy  for 
cash,  the  invalid  preferring  to  maintain  his  insurance  in 
force,  it  is  customary  for  a  company  to  retain  a  part  of 
the  reserve  pertaining  to  withdrawing  policies,  as  a 
Surrender  Charge  to  compensate  for  the  anticipated 
selection  against  the  company.     (See  page  5Q). 

In  view  of  the  guaranteed  cash  surrender  value  of 
$389.00  on  the  policy  above  described,  persons  not  versed 
in  the  scientific  principles  of  life  insurance  sometimes 
assert  that  The  Mutual  Life  is  offering  a  cash  value  of 
$78.25  in  excess  of  the  accumulated  reserve,  a  practice 
which  they  characterize  as  unwise  if  not  dangerous. 
The  answer  is  simply  that  the  cash  value  named  is  not 
in  excess  of  the  reserve  actually  held  by  the  company 
against  that  policy.  If,  for  example,  the  contract,  instead 
of  being  an  ordinary  life  of  $1,000,  were  a  twenty-year 
pure  endowment  of  $389.00,  with  term  insurance  of 
$1,000,  everyone  would  readily  understand  that  the  com- 
pany would  necessarily  hold  a  reserve  of  $389.00  at  the 
end  of  twenty  years,  since  the  reserve  must  equal  the 
face  of  the  endowment  at  the  end  of  the  endowment 
period.  Now,  although  The  Mutual  Life  contract  re- 
ferred to  is  in  form  an  ordinary  life  with  a  gross  prem- 
ium of  only  $27.88,  inasmuch  as  the  company  guarantees 

79 


to  pay  $389.00  cash  at  the  end  of  twenty  years,  the 
policy  becomes  virtually  a  twenty-year  pure  endow- 
ment for  that  amount  (besides  the  $1,000  term  insur- 
ance), and  under  the  law  the  company  is  required  to 
accumulate  against  it  a  reserve  to  the  full  amount  of  that 
endowment,  to  wit:  $389.00.  In  other  words,  every  com- 
pany is  obliged  to  maintain  a  reserve  sufficient  to  make 
good  every  guarantee  contained  in  its  contract. 

To  accumulate  a  reserve  of  $389.00  in  twenty  years 
necessarily  requires  a  larger  net  premium  than  to  accumu- 
late one  of  $310.75.  It  follows  that  the  net  premium  of 
The  Mutual  Life  policy  described  is  considerably  more 
than  $19.91,  and  the  loading  correspondingly  less 
than  $7.97. 

The  cash  values  of  The  Mutual  Life  on  deferred 
distribution  policies,  issued  since  1898  with  a  dividend 
period  of  fifteen  or  twenty  years,  which  includes  most  of 
the  business  written  between  1898  and  1907,  are  larger 
than  those  guaranteed  by  most  other  companies,  even 
though  the  latter  may  be  on  a  higher  reserve  basis  and 
collect  a  larger  gross  premium.  This  simply  means 
that  the  loading  in  the  case  of  the  Mutual  Life  policy 
under  discussion  is  less,  and  that  the  company  sets  aside 
a  somewhat  larger  part  of  the  gross  premium  for  reserve, 
and  a  somewhat  smaller  amount  for  expenses  and  con- 
tingencies. 

A  Misleading  Ratio 

The  foregoing  observations  illustrate  the  unfair 
and  misleading  character  of  such  a  ratio  as  that  of 
''Expenses  Incurred  to  Loading  Earned."     It  is  very 

10 


often  the  case  that  the  company  which  shows  the  smaller 
ratio  of  expenses  to  loading  is  able  to  do  so  by  virtue  of 
the  fact  that  it  has  a  much  larger  loading  to  start  with 
than  its  competitor.  With  the  same  gross  premium,  the 
former  may  have  a  loading  of  $7.97,  while  the  latter  has 
but  $5.00  or  $6.00.  The  former  may  have  a  saving  from 
loading,  simply  because  it  has  a  large  loading  to  begin 
with.  The  latter  may  have  no  saving  from  this  source 
and  yet  be  the  more  economically  managed  of  the  two; 
or,  it  may  have  a  very  large  saving  from  loading,  as  The 
Mutual  Life  has,  but  in  either  case  the  ratio  would  fail  to 
give  it  proper  credit. 

Net  Valuation 

The  insurance  laws  of  the  several  states  require 
every  regular  life  insurance  company  to  have  on  hand  at 
all  times  cash  or  approved  securities  not  less  in  amount 
than  the  Net  Value  of  its  outstanding  policies,  according 
to  the  Minimum  Legal  Standard  of  Valuation, 

By  Net  Value  is  meant  the  amount  of  the  reserve 
pertaining  to  the  policy  at  any  stated  time.  It  is  always 
the  difference  between  the  present  worth  of  the  net 
premiums  to  be  paid  on  the  policy,  and  the  present  worth 
of  the  benefits  guaranteed  thereunder — such  as  amounts 
payable  at  death,  at  maturity,  on  surrender,  etc. 

Net  Valuation  is  the  process  of  determining  the 
legal  net  value  or  reserve  of  a  company's  outstanding 
policies,  the  net  premium  only — not  the  gross  premium 
— being  considered.  To  understand  what  is  meant  by 
the  term  Minimum  Legal  Standard  of  Valuation, 
observe  that,  in  the  computation  of  the  premium  it  is 

81 


assumed  that  the  reserve  will  earn  a  specified  rate  of 
interest.  In  the  case  of  our  hypothetical  company  the 
rate  assumed  is  three  per  cent.  On  this  basis,  the 
required  net  annual  premium  of  an  ordinary  life  policy 
issued  at  age  fifty-six  was  found  to  be  $47.76.  The  reserve 
or  insurance  fund,  consisting  of  the  net  premium  receipts 
plus  the  interest  earned  thereon  at  the  assumed  rate, 
suffices  for  the  payment  of  all  existing  policies  at  maturity. 

It  is  obvious  that,  in  order  to  accumulate  a  specific 
sum  of  money,  as  the  reserve  of  a  life  policy,  within  a 
stated  time  by  means  of  small  yearly  deposits  or  prem- 
iums, the  deposits  must  be  larger,  and  the  fund  on  hand 
at  any  time  prior  to  age  96  must  be  greater,  if  the  interest 
to  be  added  to  the  fund  is  at  the  rate  of  only  three  per 
cent,  than  if  three  and  a  half  or  four  per  cent,  interest  is 
to  be  received.  It  is,  therefore,  equally  clear  that,  if  the 
net  premium  receipts  of  a  life  insurance  company  were 
certain  to  earn  three  and  a  half  or  four  per  cent,  interest, 
the  premium  rates  necessary  to  provide  funds  sufficient 
for  the  payment  of  all  policies  at  maturity  would  be 
smaller  than  when  it  is  assumed  that  only  three  per  cent, 
interest  will  be  realized.  In  other  words,  when  the 
reserve  is,  to  be  accumulated  at  three  per  cent,  interest, 
larger  net  premiums  are  necessary  than  when  a  higher 
interest  rate  is  assumed. 

In  all  cases,  whatever  the  rate  of  interest  assumed, 
the  reserve  at  the  attained  age  of  ninety-six  is  equal 
to  the  face  amount  of  the  policy.  Observe  that  in  our 
Verification  Table  the  reserve  at  the  end  of  the  thirty- 
ninth  year  at  the  attained  age  of  ninety-five  is  $923.11. 
That  sum  plus  the  next  year's  net  premium,  $47-76,  plus 


three  per  cent,  interest,  amounts  to  $1,000  at  the  end  of 
the  year  at  the  attained  age  of  niney-six.  Had  it  been 
assumed  in  the  computation  that  the  funds  would  earn 
four  per  cent.,  the  required  net  premium  would  have  been 
only  $45.00  instead  of  $47.76,  and  the  reserve  at  the 
attained  age  of  ninety-five  would  have  been  $916.54 , 
instead  of  $923.11.  Observe  that  $916.54,  plus  the  next 
year's  net  premium  of  $45.00,  plus  four  per  cent,  interest, 
likewise  amounts  to  $1,000  at  the  end  of  the  year  at  the 
attained  age  of  ninety-six.  Thus,  as  stated  before,  the 
higher  the  rate  of  interest  assumed,  the  smaller  will  be 
the  reserve  pertaining  to  any  policy.  A  three  and  one- 
half  per  cent,  reserve  is  larger  than  one  computed  on  a 
four  per  cent,  basis  and  smaller  than  a  three  per  cent, 
reserve. 

The  laws  of  the  several  states  prescribe  the  max- 
imum rate  of  interest  that  may  be  assumed,  and  the 
mortality  table  that  shall  be  used,  in  computing  the 
reserve  or  net  value  of  a  company's  policies.  This  re- 
quirement is  termed  the  Legal  Standard  of  Valuation. 
The  net  value  computed  by  the  legal  standard  is  termed 
the  Legal  Net  Value  or  Legal  Reserve.  In  several 
states  the  rate  of  interest  fixed  by  the  Minimum  Legal 
Standard,  or  the  lowest  standard  prescribed  by  law,  is 
four  and  one-half  per  cent. — ^in  others  four  per  cent. 
In  New  York,  Massachusetts,  and  one  or  two  other 
states,  the  minimum  legal  standard  calls  for  three  and 
one-half  per  cent,  interest,  so  that  a  company  whose 
premiums  are  computed  on  a  four  per  cent,  reserve  basis 
must,  in  order  to  do  business  in  those  states,  submit  to  a 
Valuation  by  the  higher  standard  of  three  and  one-half 


per  cent.  Many  companies,  such  as  The  Mutual  Life, 
have  recently  adjusted  their  premiums  for  new  business 
to  a  3  per  cent,  basis,  and  are  accumulating  3  per  cent, 
reserves  accordingly,  notwithstanding  the  lower  minimum 
standard  authorized  by  law. 

Determining  the  Net  Value 

Knowing  the  ages  of  the  several  policy-holders, 
we  may  determine  how  many  of  these,  according  to  the 
mortality  table,  will  die  in  each  year  thereafter,  and  how 
many  will  be  living  at  the  end  of  each  year,  and  hence 
may  compute  the  amount  of  claims  to  be  expected  in  each 
year  until  all  existing  policies  have  matured,  either  by 
the  death  of  the  policy-holder  or  the  expiration  of  the 
term  for  which  the  contract  was  written.  Having  these 
data  we  may  compute  the  present  worth  or  present  value 
of  all  outstanding  policies — that  is,  the  sum  which  ac- 
cumulated at  a  given  rate  of  interest,  say  three  per  cent., 
will  make  an  amount  sufficient  to  pay  every  policy  in  full 
as  the  policies  mature.  (See  Computation  of  Premium, 
page  12). 

In  like  manner,  knowing  how  many  policy-holders 
will  be  living  according  to  the  table  at  the  beginning  of 
each  subsequent  year,  to  pay  the  premiums  called  for  by 
the  several  policies,  we  may  determine  the  net  premium 
income  of  each  year  until  the  last  existing  policy  has 
matured.  Hence  we  may  compute  the  present  worth  of 
all  future  net  premiums  to  be  collected  on  outstanding 
policies. 

Let  us  now  take  for  illustration  the  case  of  a  com- 
pany which  has  just  issued  100,000  policies,  aggregating 

84 


a  total  of  $100,000^000  insurance.  Assume  that  the  pres- 
ent worth  of  those  policies — that  is,  the  present  worth  of 
the  benefits  to  accrue  under  their  terms,  is  found  to  be 
$37,055,000.  This  sum  then  constitutes  the  present  value 
of  the  policy  obligations  which  the  company  has  assumed. 
To  pay  these  policies  as  they  mature,  the  company  has  no 
other  certain  resource  than  the  net  premiums  stipulated 
to  be  paid  thereon  plus  the  interest  which  those  premiums 
will  earn  at  the  assumed  rate,  say  three  per  cent.  If  now 
the  present  worth  of  these  premiums  is  likewise  found  to 
be  $37,055,000,  it  is  obvious  that  the  company  is  solvent 
and  will — if  three  per  cent,  interest  is  earned  and  the 
mortality  does  not  exceed  that  indicated  by  the  table — 
be  able  to  meet  its  obligations  at  maturity.  A  statement 
of  its  assumed  condition  would  be  as  follows: 

Credit  Side. 

Present  worth  of  net  premiums  to  be  collected 

on  existing  contracts    $37,055,000 

Debit  Side, 

Present  worth  of  benefits  under  outstanding 

policies    $37,055,000 

Such  would  be  the  exact  status  of  a  legally  solvent 
mutual  company  the  day  it  begins  business,  after  a 
number  of  policies  have  been  written  but  before  any 
premiums  have  been  collected. 

Let  us,  however,  take  the  same  company  after 
several  years'  premiums  have  been  collected  and  a  number 
of  policies  paid,  a  reasonable  amount  of  new  business 
having  been  written  in  the  meantime.  As  some  of  the 
net  premiums  called  for  by  existing  contracts  have  been 


received  and  disbursed,  the  present  worth  of  the  premiums 
remaining  to  be  collected  will  no  longer  equal  the  present 
worth  of  benefits  under  policies  now  outstanding.  Assume, 
for  example,  the  present  worth  of  those  benefits  to  be  now 
$38,000,000,  and  the  present  worth  of  future  net  premi- 
ums, $34,000,000.  The  present  worth  of  benefits 
promised,  or  obligations  assumed,  will  be  larger  than  at 
first,  because  every  existing  policy  is  nearer  maturity, 
while  the  present  worth  of  net  premiums  to  be  collected 
in  the  future  will  be  less  than  before,  because  some  part 
of  the  premiums  originally  called  for  by  every  existing 
policy  have  already  been  collected.  Our  debits  then  in 
this  case  would  exceed  our  credits  by  $4,000,000,  and 
the  statement  would  now  be  as  follows: 

Credit  Side 

Present  worth  of  net  premium;s  to  be  collected 

on  existing  policies    $34,000,000 

Deficit    4,000,000 

$38,000,000 
Debit  Side 

Present  worth  of  benefits  under  outstanding 

policies   $38,000,000 

The  company  is  now  clearly  insolvent  under  the 
law,  for  the  present  worth  of  net  premiums  to  be  received 
— its  only  apparent  resources — is  $4,000,000  less  than 
the  present  worth  of  the  benefits  to  be  paid.  This  deficit 
represents  the  Legal  Reserve  Liability  of  the  company 
— that  is,  the  Net  Value  of  its  outstanding  policies  ac- 
cording to  the  legal  standard  of  valuation,  being  the  dif- 
ference between  the  present  worth  of  the  benefits  for 
which  the  company  is  liable  under  its  policies,  and  the 


present  worth  of  all  the  net  premiums  to  be  received.  If 
the  company,  however,  after  providing  for  the  tabular 
mortality  and  matured  endowments,  has  reserved  from 
year  to  year  the  balance  of  its  net  premium  and  interest 
income,  the  funds  so  reserved  will  now  aggregate  exactly 
the  amount  of  the  computed  reserve  liability.  In  other 
words,  it  will  have  on  hand  the  reserve  required  by  law 
to  maintain  solvency,  and  the  statement  of  its  condition 
will  now  assume  the  following  form: 

Credit  Side 

Present  worth  of  net  premiums  remaining  to 

be  collected  on  existing  policies $34,000,000 

Reserve  (cash  and  invested  funds) 4,000,000 

$38,000,000 
Debit  Side 

Present  worth  of  benefits  contracted  for  in 

outstanding  policies    $38,000,000 

This  suggests  the  definition  of  the  legal  reserve 
given  above,  to  wit:  "A  fund  equal  in  amount  to  the 
excess  of  the  present  value  of  benefits  under  outstanding 
policies  over  the  present  value  of  net  premiums  to  be 
paid  on  those  policies.*' 

On  the  basis  of  the  statement  as  last  rendered, 
the  company  is  technically  solvent,  since  the  credits  and 
debits  are  equal.  The  form  of  the  statement  may  be 
simplified  by  eliminating  the  two  items,  "Present  worth 
of  net  premiums'*  and  ''Present  worth  of  policies,"  and 
simply  carrying  to  the  debit  side  of  the  account  the 
difference  between  the  present  worth  of  policy  obligations 
and  the  present  worth  of  premiums  to  be  collected,  which 

87 


is  the  company's  legal  reserve  liahility,  or  the  net  value 
of  the  benefits  guaranteed  under  its  outstanding  policies. 
As  the  company  holds  cash  and  invested  funds  to  the 
amount  of  this  liability,  the  statement  will  assume  the 
following  form: 

Credit  Side 
Cashj  invested  funds,  and  credits  (Assets)  . .  .  $4,000,000 

Debit  Side 
Net  value  of  all  outstanding  policies  (L2a6z7i%)  $4,000,000 

The  Test  of  Solvency 
The  comparison  of  a  company's  Admitted  Assets 
— money,  invested  funds  and  valid  credits  approved  by 
the  insurance  authorities — with  its  total  liabilities  consti- 
tutes the  legal  test  of  its  solvency.  By  the  financial  state- 
ment last  above  set  out,  the  company  in  question  is  legally 
solvent — its  assets  being  exactly  equal  to  its  liabilities; 
nevertheless,  a  company  in  just  that  condition  would  in 
fact  be  upon  the  verge  of  bankruptcy,  for  the  loss  of  a 
small  amount  by  depreciation  of  values,  extra  mortality, 
or  other  cause,  would  render  it  insolvent  under  the  law. 
Such  being  the  case,  it  is  of  the  first  importance  for  every 
company  to  maintain  as  a  margin  of  safety  an  additional 
fund  in  excess  of  all  legal  liabilities,  variously  termed 
"surplus,"    "indivisible    surplus,"    "unassigned    funds," 
etc.    Under  the  New  York  law  this  extra  fund  or  margin 
of  safety  is  called  the  Contingency  Reserve.     Assuming 
that  the  company  in  question  has  such  additional  funds 
to  the  amount  of  $1,000,000,  a  statement  of  its  financial 
condition  would  then  read : 


Admitted  Assets 
Cash,  invested  funds,  and  credits $5,000,000 

Liabilities 

Net  value  of  all  outstanding 

policies     $4,000,000 

Contingency  reserve  (surplus) .  .    1,000,000     $5,000,000 

A  Misleading  Ratio 

In  the  above  case,  a  loss  of  assets  in  excess  of 
$1,000,000  would  sweep  away  the  contingency  reserve 
and  render  the  company  insolvent.  The  smaller  the 
amount  of  such  additional  fund,  the  more  imminent  the 
danger.  It  is  obvious,  therefore,  that  the  measure  of  a 
company's  strength  is  to  be  gauged  rather  by  the  amount 
of  extra  or  surplus  funds  which  it  holds  in  addition  to 
the  legal  reserve  or  net  value  of  its  outstanding  policies, 
than  by  the  percentage  which  such  extra  funds  are  of 
the  total  liabilities,  i.  e.,  the  company's  "Ratio  of  Assets 
to  Liabilities."  For  example:  According  to  the  statistics 
for  1914,  a  certain  company  of  well-known  excellence 
had  surplus  funds  at  the  end  of  that  year  of  more  than 
$4,000,000,  and  a  ratio  of  admitted  assets  to  liabilities  of 
106.5;  that  is,  its  assets  exceeded  its  liabilities  by  only 
6J4  per  cent. 

On  the  other  hand,  the  assets  of  a  smaller  company  of 
considerable  prominence  exceeded  its  liabilities  by  twenty- 
nine  per  cent.,  yet  its  total  surplus  funds  were  less 
than  $130,000.  Assuming  that  the  assets  in  each  case 
were  of  the  highest  class,  there  can  be  no  doubt  as  to  the 

89 


relative  strength  of  the  two  organizations — the  fact  being 
the  reverse  of  what  might  be  inferred  if  only  the  ratios 
cited  were  to  be  considered.  A  surplus  of  only  $130,000 
might  readily  be  wasted  or  lost  in  a  single  transaction — 
far  more  readily,  it  will  be  conceded,  than  a  surplus  of 
more  than  $4,000,000.  A  still  more  striking  illustration 
of  the  misleading  character  of  this  ratio  is  afforded  by  the 
figures  of  a  still  smaller  company  with  a  ratio  of  assets  to 
liabilities  of  592  and  a  total  surplus  of  less  than  $21,000. 

Reserve  Basis  Must  Be  Considered 

There  is  another  test,  however,  that  is  too  often 
overlooked  by  the  ordinary  insurance  man  as  well  as  by 
the  insuring  public,  and  that  is  the  question  of  reserves. 
Let  us  compare  two  companies,  A  and  B,  assuming  that 
each  has  $100,000,000  of  insurance  in  force,  all  issued 
10  years  ago,  at  age  40,  on  the  ordinary  life  plan.  Let 
us  also  assume  that  each  company,  by  the  valuation  of 
the  insurance  department,  shows  a  surplus  of  $1,000,000, 
The  natural  assumption  would  be  that  the  two  companies 
are  of  equal  strength,  but  this  does  not  necessarily  fol- 
low. Neither  company  knows  in  advance  what  rate  of 
interest  will  be  earned  during  the  entire  existence  of  its 
outstanding  policies.  In  order  to  be  on  the  safe  side. 
Company  A  assumes  that  it  will  earn  as  little  as  Syi 
per  cent,  and,  accordingly,  it  must  create  and  maintain  a 
reserve  or  insurance  fund  which,  with  future  net  prem- 
iums received  and  interest  added  thereto  yearly  at  3J/$ 
per  cent.,  will  suffice  for  the  payment  of  all  accruing 
claims  each  year  until  the  total  of  $100,000,000  has  been 

90 


paid.  Company  B,  still  more  conservative,  bases  its 
calculations  upon  earning  only  3  per  cent.  Accordingly, 
it  must  create  and  maintain  a  reserve  which,  with  future 
net  premiums  received  and  only  3  per  cent,  interest  added 
thereto  yearly,  shall  likewise  be  sufficient  for  the  pay- 
ment of  all  accruing  claims,  until  the  total  of  $100,- 
000,000  has  been  paid.  As  both  companies  are  to  pay 
the  same  amount  ultimately,  it  is  obvious  that  Company 
B,  which  adds  only  3  per  cent,  to  its  reserve  each  year, 
must  at  all  times  maintain  a  larger  fund  than  Company 
A,  which  adds  S^^  per  cent,  yearly.  This  illustrates  the 
fact  that  a  3  per  cent,  reserve,  at  any  and  every  date 
until  the  last  policy  matures,  must  be  larger  than  a 
reserve  based  on  3J^  per  cent. 

Tabulated  Illustration 

Each  company  has  $100,000,000  of  outstanding 
policies  all  written  10  years  ago  at  age  40.  Turning  to 
your  reserve  tables  you  will  find  that  the  reserve  of  an 
ordinary  life  policy  issued  ten  years  ago  at  age  40  on  a 
8j^  per  cent,  basis  would  amount  now  to  $166.89  per 
$1,000,  and  on  100,000  policies  of  $1,000  each,  the  total 
reserve  would  be  $16,689,000.  The  reserve  tables  also 
show  that  the  3  per  cent,  reserve  of  an  ordinary  life 
policy  issued  ten  years  ago  at  age  40  would  now  be 
$177.20  per  $1,000,  while  the  total  reserve  on  100,000 
policies  of  $1,000  each  would  be  $17,720,000,  the  amount 
held  by  Company  B.  As  each  company  has  $1,000,000 
of  surplus,  the  financial  statement  in  each  case  would 
be  as  follows: 

91 


Company  A 

Reserve,  3J/^   per  cent $16,689,000 

Surplus    1,000,000 

Total   Assets $17,689,000 

Company  B 

Reserve,  3  per  cent $17>720,000 

Surplus    1,000,000 

Total  Assets $18,720,000 

Company  B's  reserve  exceeds  that  of  Company  A 
by  $1,031,000;  but,  if  a  3^/^  per  cent,  reserve  is  large 
enough  for  Company  A,  it  should  be  large  enough  for 
Company  B.  If,  therefore,  we  value  the  latter  com- 
pany's business  on  a  basis  of  3J/2  per  cent.,  the  excess  in 
the  reserve  of  Company  B  will  be  transferred  to  surplus, 
and  the  two  financial  statements  will  stand  as  follows : 

Company  A 

Reserve,  3j4   per  cent $16,689,000 

Surplus    1,000,000 

Total  Assets $17,689,000 

Company  B 

Reserve,  3^   per  cent $16,689,000 

Surplus    2,031,000 

Total  Assets $18,720,000 

It  now  appears   that  our   3  per  cent,   company, 
valued  on  a  3  3^  per  cent,  basis,  the  same  as  Company  A, 


has  a  surplus  more  than  double  that  of  the  latter  com- 
pany. It  is  obvious,  therefore,  that,  in  quoting  surplus 
as  a  test  of  strength,  the  reserve  basis  must  be  considered. 
With  equal  surpluses,  the  3  per  cent,  company  will  be 
stronger  than  one  on  a  3J/2  per  cent,  basis;  and  the 
former  may  even  have  the  smaller  surplus  and  yet  be 
the  stronger  company.  In  the  foregoing  examples.  Com- 
pany B  valued  on  a  3  per  cent,  basis,  might  show  a  sur- 
plus of  less  than  half  a  million — indeed,  it  might  show 
no  surplus  at  all — and  yet  be  stronger  than  Company  A; 
for,  in  the  latter  case,  on  a  Sy^  per  cent,  valuation,  it 
would  still  have  a  surplus  of  $1,031,000  against  a  surplus 
of  $1,000,000  for  Company  A. 

Another  extremely  important  point  as  between  different 
reserve  bases  is  this:  A  3  per  cent,  company  will  make 
surplus  more  rapidly  than  a  S^^  or  4  per  cent,  company. 
For  example:  suppose  companies  A  and  B  both  to  be 
earning  a  net  rate  of  4J/2  per  cent,  interest.  All  interest 
earned  by  Company  A  in  excess  of  3j/2  per  cent. — that 
is,  one  per  cent. — becomes  surplus,  while  Company  B 
has  the  excess  over  3  per  cent. — that  is,  one  and  one-half 
per  cent. — or  one-half  more  than  Company  A.  It  is 
obvious  that  Company  B  will  the  more  quickly  recover 
from  unexpected  losses,  will  the  more  quickly  restore  a 
depleted  surplus,  and  the  more  readily  withstand  any 
unusual  strain. 

Several  modifications  of  the  system  of  net  valua- 
tion described  in  the  foregoing  pages  have  been  estab- 
lished by  recent  legislation  and  will  be  explained  in  a 
later  chapter.     (Page  119  et  seq.) 


08 


The  Annual  Statement- 

The  laws  of  the  several  states  require  every  regu- 
lar life  insurance  company  to  file  with  the  insurance 
department  in  every  year  as  of  the  date  of  December  SI, 
a  sworn  statement  of  its  assets  and  liabilities^  including 
the  legal  net  value  or  reserve  of  all  outstanding  policies 
as  determined  by  the  minimum  standard  of  valuation. 
As  every  such  company  is  required  under  the  law  to 
maintain  at  all  times  a  reserve  not  less  in  amount  than 
the  net  value  of  all  policies  in  force,  such  organizations 
are  called  *'Legal  Reserve"  companies.  They  are  also 
sometimes  termed  *'Old  Line"  to  distinguish  them  from 
Co-operative,  Stipulated  Premium,  Fraternal,  and  other 
assessment  organizations  whose  premium  rates  or  assess- 
ments are  not  fixed,  but  are  subject  to  increase  as 
experience  may  demand.  These  assessment  societies  are 
not  required  by  law  to  maintain  an  adequate  reserve,  nor 
are  they  subjected  to  any  standard  system  of  valuation  to 
determine  their  solvency  or  the  sufficiency  of  their  rates, 
save  that  in  certain  states  fraternal  societies  must  submit 
to  valuation,  although  jnot  yet  required  to  maintain 
mathematical  solvency.  So  long  as  the  funds  on  hand 
are  sufficient  to  meet  accrued  death  claims,  little  or  noth- 
ing more  is  required  of  them.  Future  deficits  are  to  be 
met  by  an  increase  of  rates  or  a  scaling  down  of  death 
benefits,  but  the  members  of  such  assessment  societies 
are  prone  to  regard  the  probability  of  such  a  contingency 
as  quite  remote. 


M 


chapter  ix 
Gains  or  Savings  in  Life  Insurance 

TN  the  computation  of  the  premium  it  was  assumed  that 
the  mortality  of  our  hypothetical  company  would 
correspond  with  the  American  Experience  Table  and  that 
our  funds  would  earn  just  three  per  cent,  interest.  Upon 
this  hypothesis  the  net  premium  is  precisely  sufficient  for 
the  payment  of  all  claims  that  may  accrue.  It  follows  that 
if  the  mortality  of  the  company  should  exceed  that  of  the 
table,  and  the  rate  of  interest  earned  should  be  less  than 
that  assumed,  our  premium  would  be  inadequate  and  our 
reserve  would  fall  short  of  the  requirements.  It  would 
be  impossible,  however,  to  construct  an  infallible  table — 
one  that  would  indicate  with  absolute  accuracy  the 
mortality  to  be  experienced.  Inasmuch  then  as  our  actual 
death  rate  will  certainly  differ  somewhat  from  the  tabular, 
it  is  of  the  first  importance  that  the  variation  be  on  the 
side  of  safety — a  lower  rather  than  a  higher  mortality. 
Accordingly,  in  the  construction  of  the  table  all  doubts 
have  been  resolved  in  favor  of  this  position,  with  the 
result  that  in  practice  the  mortality  experience  of  every 
well-managed  company  is  less  than  that  indicated  by  the 
table  upon  which  its  premium  rates  are  based.  In  like 
manner,  as  heretofore  explained,  it  is  morally  certain 
that  the  actual  interest  earnings  will  be  in  excess  of  the 
rate  assumed,  so  that  in  practice  there  will  be  a  gain 
from  both  sources  named,  and  our  receipts  will  be  in 
excess  of  the  amount  required  to  meet  our  obligations. 

96 


Sources  of  Gain 

To  the  end  that  the  comments  following  may  be 
readily  comprehended,  it  is  suggested  that  the  reader 
keep  the  Verification  Table  (pages  46  and  47)  before 
him  for  constant  reference. 

Saving  in  Mortality 

In  our  hypothetical  company  of  63,364  members, 
all  of  the  age  of  fifty-six,  we  have  made  provision  for 
1,260  deaths  the  first  year,  that  being  the  tabular  mor- 
tality. As  each  member  is  insured  for  $1,000,  the 
expected  death  claims  will  amount  to  $1,260,000.  Let 
us  assume  now  that  the  actual  deaths  number  only  1,160, 
making  actual  death  claims  $1,160,000,  or  $100,000  less 
than  was  counted  upon  and  provided  for  in  the  premiums 
collected.  The  actual  saving  in  mortality,  however,  is 
not  $100,000;  for  at  the  end  of  the  year,  at  the  attained 
age  of  fifty-seven,  we  shall  have  62,204  members  living 
instead  of  62,104.  The  100  additional  lives  must  be 
paid  for  ultimately,  and  in  the  valuation  of  its  assets  and 
liabilities,  the  company  will  be  charged  with  a  terminal 
reserve  of  $29.90  for  each  of  these  lives,  making  an 
additional  reserve  liability  of  $2,990.  This  sum  being 
deducted  from  the  $100,000  of  death  claims  saved,  makes 
the  actual  saving  in  mortality  $97,010.  In  other  words, 
the  saving  in  mortality  consists,  not  of  the  face  amount  of 
death  claims  saved,  but  of  the  amount  at  risk  pertaining 
to  those  claims.  In  the  case  of  our  hypothetical  company 
the  amount  at  risk  on  each  life  during  the  first  policy 

96 


year  is  $970.10.  (See  page  67.)  With  one  hundred 
fewer  deaths  than  were  expected,  the  saving  in  mortality 
will  be  $970.10  x  100  =  $97,010. 

The  Actual  Saving 

The  beginner  is  sometimes  puzzled  at  this  stage 
by  a  problem  which  suggests  itself  in  the  following  form : 
Referring  to  the  saving  in  mortality  of  $97,010  in  our 
first  year,  has  this  amount  really  been  saved,  or  has  its 
payment  simply  been  deferred.''  After  all,  the  one  hun- 
dred lives  are  still  with  the  company  and  will  pass  away 
within  the  limit  of  life,  some  very  shortly,  others  after 
many  years;  and  the  policies  represented  by  them  must 
ultimately  be  paid.  Instead  of  an  actual  saving  of 
$97,010  then,  do  we  not  in  reality  save  merely  the 
interest  on  the  $100,000  of  death  claims  whose  payment 
has  been  deferred? 

You  have  seen  by  the  Verification  Table  that  for 
each  of  the  62,104  members  living  at  the  end  of  the  first 
year  at  the  attained  age  of  fifty-seven,  we  hold  a  terminal 
reserve  of  $29.90,  and  that  these  accumulated  reserves 
plus  the  future  net  premiums  to  be  received,  will  provide 
funds  exactly  sufficient  for  the  payment  of  all  existing 
policies  as  they  mature.  If  this  is  true  of  62,104  mem- 
bers, it  will  likewise  be  true  of  62,204,  or  of  100,000,  or 
of  any  other  large  number.  We  have  therefore  had  an 
actual  saving  in  mortality  of  $97,010,  and  have  accumu- 
lated an  actual  profit  or  gain  of  that  amount,  since  for 
each  of  the  62,204  members  of  the  age  of  fifty-seven  now 
belonging  to  the  company,  we  hold  a  reserve  of  $29.90, 
and  are  to  collect  from  each  a  net  premium  of  $47.760895 

87 


every  year  hereafter,  even  as  in  the  case  of  the  original 
number  of  62,104. 

To  illustrate  further:  let  us  take  the  case  of  the 
twenty-one  members  living  at  the  age  of  ninety-four. 
Assume  that  there  will  be  seventeen  deaths  instead  of 
eighteen,  a  saving  of  one.  As  the  terminal  reserve  on 
one  life  is  $923.11,  the  amount  at  risk  will  be  $76.89, 
which  will  accordingly  be  the  saving  in  mortality.  The 
four  lives  now  remaining  will  begin  the  next  year  at  the 
attained  age  of  95,  and,  according  to  the  table,  none  of 
these  will  live  beyond  the  end  of  that  year,  or  beyond 
the  attained  age  of  96.  The  payment  of  the  claim  on  the 
fourth  life,  therefore,  is  simply  deferred  for  one  year. 
Does  it  not  seem,  then,  that  the  saving  in  mortality  will 
be  merely  the  interest  on  $1,000  for  one  year,  to  wit: 
$30,  instead  of  the  amount  at  risk,  $76.89.? 

Let  us  see  how  it  works  out.  Taking  age  ninety- 
four,  we  have  now  four  members  living  at  the  end  of  the 
year,  at  the  attained  age  of  ninety-five,  instead  of  three, 
and  we  shall  accordingly  have  a  total  reserve  of  $3,692.45 
(making  due  allowance  for  decimal  correction),  instead 
of  $2,769.34.  ($2,769.34  -f  $923.11  =  $3,692.45). 
Modifying  the  Verification  Table  accordingly,  the  opera- 
tions of  the  last  year  may  be  tabulated  as  follows: 

Net  Premium  Income  at  age  95  ($47.760895x4)      $191.04 
Add  Terminal  Reserve  of  preceding  year....    3,692.45 

Initial  Reserve,  age  95 $3,883.49 

Add  one  year's  interest  at  three  per  cent.,.  ...       116.51 

Terminal  Reserve,  attained  age  of  96 $4,000.00 

The  result  proves  that  the  saving  in  mortality  is 
measured  by  the  amount  at  risk,  and  not  by  the  interest 
earned  on  the  face  of  deferred  death  claims. 


When  Saving  in  Mortality  is  Greatest 

Experience  has  shown  that  the  saving  in  mortality- 
will  be  greatest  in  the  case  of  business  most  recently 
written,  owing  to  the  culling  out  of  impaired  lives  by 
medical  examination.  For  instance,  the  mortality  in  the 
first  year  of  insurance  is  rarely  so  much  as  fifty  per  cent, 
of  the  tabular  rate,  and  is  much  less  than  the  normal  for 
several  years  longer.  The  benefit  derived  from  medical 
selection,  however,  is  commonly  assumed  to  be  lost 
within  about  five  years,  and  much  the  greater  part  of 
it  undoubtedly  does  accrue  within  that  period.  This 
does  not  mean  that  a  thousand  lives,  five  years  after 
medical  examination,  would  average  no  better  physically 
than  a  like  number  of  new  risks,  accepted  without  any 
examination  at  all.  Any  company  which  might  adopt 
the  latter  course  would  be  quickly  overwhelmed  with 
impaired  lives  that  would  not  ordinarily  apply  for  insur- 
ance because  conscious  of  their  inability  to  pass  an 
examination. 

A  Misleading  Ratio 

The  low  death  rate  in  the  years  immediately  suc- 
ceeding medical  examination  is  instrumental  in  effecting 
a  large  saving  in  mortality  in  the  case  of  new  companies, 
and  of  old  companies  writing  a  large  new  business.  While 
this  saving  in  mortality  is  largely  offset  by  the  increase  in 
the  expense  account,  owing  to  the  relatively  large  cost  of 
new  business,  it  is  also  true  that  the  new  company,  or  the 
company  writing  a  large  new  business  will  necessarily 
show  a  comparatively  high  expense  ratio,  owing  to  the 


large  outlay  for  commissions  and  other  items  of  initial 
cost,  but  this  increased  expense  may  be  more  than  offset 
by  the  increased  saving  in  mortality.  The  facts  cited 
simply  indicate  the  inevitably  misleading  character  of  an 
expense  ratio  which  fails  to  take  into  account  com- 
pensating conditions. 

Inasmuch  as  a  low  mortality  is  incidental  to  all 
new  business  and  therefore  to  all  new  companies,  whether 
assessment  or  "old  line,"  the  absurdity  of  citing  it  as 
something  phenomenal,  and  as  evidence  of  extraordinary 
care  in  selection  of  risks,  is  apparent.  It  is  undoubtedly 
true  that  careful  selection  will  go  far  toward  increasing 
the  saving  in  mortality ;  but  it  is  likewise  true  that  the 
low  death  rate  of  the  new  company  is  mainly  attributable 
to  the  fact  that  is  is  new,  its  members,  or  a  large  pro- 
portion of  them,  being  fresh  from  the  medical  examiner's 
hands. 

In  addition  to  saving  in  mortality  and  excess  of 
interest  earned,  there  may  be  gains  from  other  sources, 
though  in  a  less  degree.  The  loading  for  expenses  and 
contingencies  may  be  in  excess  of  the  requirements,  or 
there  may  be  an  apparent  saving  by  reason  of  reserves 
released  on  lapsed  and  surrendered  policies.  The  word 
"apparent"  is  used  because  such  savings  are,  under 
modern  conditions,  rarely  more  than  enough,  even  if 
enough,  to  defray  the  expense  of  replacing  the  risks  with 
new  lives. 

Lapses  Not  a  Desirable  Source  of  Profit 
If  all  life  or  endowment  policies  written  were  to 
lapse  at  the  end  of  two  years,  the   forfeited  reserves 
might  constitute  an  important  source  of  profit;  or  if  all 

100 


policies  were  certain  to  lapse  at  the  end  of  three  or  four 
years  and  not  sooner^  there  would  doubtless  be  a  profit 
from  that  source,  notwithstanding  a  surrender  value  is 
allowed  at  the  end  of  the  third  year.  The  amount  that 
may  be  withdrawn  at  the  earlier  years  is  usually  less  than 
the  full  reserve,  a  part  of  the  latter  being  retained  by 
the  company  as  a  Surrender  Charge,  Although  so  much 
of  the  reserve  as  may  be  forfeited  in  the  case  of  a  lapsed 
or  surrendered  policy  is  technically  termed  a  "gain"  and 
necessarily  appears  as  such  in  the  company's  annual 
statement,  this  supposed  gain  is  largely  or  wholely  offset 
by  the  fact  that  it  is  ordinarily  the  sound  lives  that  lapse 
or  withdraw.  The  man  about  to  die,  or  whose  health  has 
become  impaired,  clings  to  his  insurance.  Thus  lapses 
naturally  tend  to  increase  the  normal  proportion  of  in- 
valids and  impaired  lives  in  a  company,  resulting  in  an 
increased  mortality.  This  is  certain  to  be  the  case  when 
the  number  of  withdrawals  is  excessive  through  loss  of 
confidence  in  the  company  or  dissatisfaction  with  the 
management.  This  tendency  of  sound  lives  to  withdraw 
and  of  impaired  lives  to  maintain  their  insurance  in  force, 
or  to  seek  new  or  more  insurance,  merely  because  they 
are  in  impaired  health,  is  termed  Selection  Against  the 
Company,  or  Adverse  Selection.  On  the  other  hand, 
some  extended  observations  would  indicate  that  when 
lapsing  is  normal — not  unduly  stimulated  by  special 
causes — the  withdrawals  as  a  class  may  be  little  or 
not  at  all  better  than  the  risks  remaining.  Neverthe- 
less, the  generally  accepted  theory  is,  that  lapses  tend  to 
a  deterioration  of  the  business,  and  it  is  always  a  question 
of  grave  concern  to  the  company  whether  the  surrender 
charge  exacted  is  sufficient  to  compensate  for  the  adverse 
selection. 

101 


Lapses  and  Termination  by  Expiry 

It  should  be  noted  here  that  some  companies  give 
an  extended  insurance  surrender  value  at  the  end  of  the 
first  year,  or  even  at  the  end  of  the  first  quarter.  If  the 
premium  is  not  paid  and  the  policy  is  not  surrendered 
for  cash  or  paid-up  value,  the  insurance  is  not  entered  on 
the  books  as  lapsed,  but  becomes  automatically  a  paid-up 
term  policy  good  for  a  brief  period,  at  the  end  of 
which,  if  not  reinstated,  it  terminates  by  expiry. 
In  some  cases  a  small  cash  value  is  offered,  even  after 
the  payment  of  but  one  quarterly  premium.  By  this 
means  the  apparent  number  of  lapses  or  withdrawals, 
most  of  which  occur  during  or  at  the  end  of  the  first 
year,  is  very  greatly  diminished.  The  reader  will  per- 
ceive the  absurdity  of  comparing  the  figures  of  official 
reports  as  to  "lapsed  and  surrendered'*  policies,  unless 
this  class  of  terminations  be  included. 

Slight  Gains  from  Saving  in  Mortality  at  the  Older 

Ages 

Recent  observations  tend  to  show  that  improved 
sanitary  conditions  and  the  great  advances  made  in 
modern  medical  science  and  surgery,  have  increased 
somewhat  the  average  length  of  human  life.  The  prob- 
able effect  has  been  to  prolong  the  lives  of  many  who, 
under  former  conditions,  would  have  succumbed  in  child- 
hood or  youth  to  the  effects  of  disease  or  injury.  In  the 
case  of  insured  lives  doubtful  risks  are  eliminated,  but  as 
the  accepted  lives  grow  older  the  benefits  of  medical 
selection  gradually  disappear,  and  we  find  the  actual 
mortality  approaching  more  nearly  to  the  tabular.     For 

102 


this  reason  it  may  be  anticipated  that  the  saving  in  mor- 
tality will  be  slight  in  the  case  of  insurance  that  has  been 
long  in  force.  As  a  matter  of  fact  and  for  another  reason, 
the  saving  in  mortality  does  steadily  decrease  with  the 
age  of  the  policies,  even  though  the  actual  death  rate  of 
the  company  continues  to  be  much  below  the  normal. 
This  is  because  the  saving  is  measured  by  the  amount  at 
risk,  and  not  by  the  face  of  the  claim.  To  illustrate: 
referring  to  the  table  on  page  67,  showing  the  amount 
at  risk  in  the  case  of  an  ordinary  life  policy  issued  at  age 
fifty-six,  assume  the  actual  mortality  for  a  series  of  years 
to  be  $1,000  less  than  the  tabular.  The  saving  in  mor- 
tality then  will  be  $970.10  in  the  first  year  at  age  fifty- 
six,  $562.75  at  age  seventy,  $323.58  at  age  eighty,  and 
$127.82  at  age  ninety. 

Savings  Vary  According  to  Reserve  Basis, 

The  savings  or  gains  will  vary  according  to  the 
reserve  basis,  the  gain  from  interest  being  greater  in 
case  of  a  three  than  of  a  three  and  a  half  or  four  per 
cent,  reserve.  To  illustrate,  for  example,  the  gain  from 
interest  earned  in  excess  of  the  assumed  rate,  suppose  the 
rate  actually  earned  to  be  5  per  cent.  The  gain  in  the 
case  of  a  three  per  cent,  reserve  will,  then,  be  two  per 
cent.,  against  one  per  cent.,  on  a  four  per  cent,  basis.  In 
the  former  case  there  is  not  only  a  larger  percentage  of 
gain,  but  it  is  a  percentage  of  a  larger  sum,  since  a  three 
per  cent,  reserve  is  larger  than  a  four  per  cent,  reserve. 

On  the  other  hand,  inasmuch  as  the  amount  at 
risk  is  less  in  the  case  of  a  three  per  cent,  reserve,  the 
saving  in  mortality  will  likewise  be  less  than  on  a  four 

103 


per  cent,  basis.  For  example:  at  age  fifty-six  the  three 
per  cent,  reserve  at  the  end  of  the  first  year  is  $29.90  and 
the  amount  at  risk  (saving  in  mortality  in  case  of  one 
death  less  than  expected)  $970.10,  while  the  four  per 
cent,  reserve  is  $27.46,  making  the  saving  in  mortality 
$972.54*.  The  difference,  however,  will  not  be  great  in 
comparison  with  gain  from  interest,  for  the  variation  in 
amount  at  risk  will  be  but  slight  in  the  earlier  years, 
when  the  accumulated  reserves  are  small;  while  at  the 
older  ages,  when  the  actual  death  rate  approaches  more 
nearly  the  tabular,  and  the  saving  in  mortality  is,  for 
that  reason,  little  or  nothing,  the  reserves  are  large  and 
the  gain  from  interest  more  pronounced. 

To  illustrate  this  subject  more  fully,  consider  the 
case  of  one  thousand  persons  all  of  the  age  fifty-six 
insured  for  $1,000  each  on  the  ordinary  life  plan.  The 
three  per  cent,  reserve  at  the  end  of  the  first  year  would 
be  $29.90  on  each  policy,  and  the  amount  at  risk  $970.10. 
The  expected  number  of  deaths  in  these  one  thousand 
lives  according  to  the  table  would  be  19.88,  and  the 
total  expected  death  claims  $19,880.  (See  "Death  Rate 
per  1,000,"  mortality  table,  page  13).  Assuming  the 
actual  death  rate  in  the  first  year  to  be  fifty  per  cent, 
of  the  tabular,  the  actual  number  of  deaths  would  be 
9.94  and  the  actual  mortality  $9,940.  That  is,  the  num- 
ber of  deaths  would  be  9.94  less  than  expected,  and  as 
the  amount  at  risk  (saving  in  mortality)  in  each  case  is 
$970.10,  the  total  saving  in  mortality  would  be  $970.10 
multiplied  by  9.94,  or  $9,642.79. 

On  a  four  per  cent,  basis  in  the  same  company 
the  reserve  on  a  single  policy  would  be  $27-46  and  the 

104 


amount  at  risk  $972.54.  The  total  saving  in  mortality, 
therefore,  would  be  $972.54  multiplied  by  9.94,  or 
$9,667.05.  That  is,  in  the  case  of  these  one  thousand 
policies  the  total  saving  in  mortality  on  a  four  per  cent, 
basis  would  be  just  $24.26  more  than  in  the  case  of  a 
three  per  cent,  reserve. 

Let  us  now  consider  the  gain  from  interest  in  the 
same  case.  The  three  per  cent,  initial  reserve  on  a  single 
policy  in  its  first  year  being  $47.76  (net  premium),  the 
total  reserve  on  one  thousand  policies  at  the  beginning 
of  the  first  year  would  be  $47,760.  Assuming  that  the 
actual  interest  earned  is  five  per  cent.,  the  total  gain 
from  interest  during  the  year  would  be  two  per  cent, 
computed  on  a  total  initial  reserve  of  $47,760,  or  $955.20. 
The  total  four  per  cent,  initial  reserve  would  be  $45,000, 
and  the  gain  from  interest  would  be  one  per  cent,  of  that 
amount,  or  $450.00,  being  $505.20  less  than  in  the  case 
of  the  three  per  cent,  reserve. 

Let  us  see  now  how  it  would  be  at  the  end  of  the 
year  in  which  the  insured  reaches  the  age  of  seventy 
years.  Of  1,000  persons  living  at  fifty-six,  609  would 
still  be  living  at  seventy  according  to  the  table,  and  of 
these  the  expected  number  of  deaths  within  a  year  would 
be  37.76.  On  policies  more  than  five  years  old,  it  is 
generally  assumed  that  the  actual  death  rate  will  be 
approximately  the  same  as  the  tabular.  In  that  case 
there  would  be  virtually  no  saving  in  mortality  at  all; 
but  let  us  assume,  for  the  sake  of  illustration,  that  the 
actual  number  of  deaths  in  this  case  will  be  two  less 
than  the  tabular.  As  the  three  per  cent,  terminal  reserve 
on  such  a  policy  for  the  fifteenth  year  would  be  $437.25, 

106 


the  amount  at  risk  would  be  $562.75.  The  saving  in  mor- 
tality^ therefore,  would  be  just  $562.75  for  each  of  the 
two  risks  saved,  or  a  total  of  $1,125.50.  On  the  other 
hand,  the  four  per  cent,  terminal  reserve  would  be 
$416.39,  the  amount  at  risk  $583.61,  and  the  saving  in 
mortality  also  $583.61  for  each  life  saved,  a  total  of 
$1,167.22,  or  $41.72  more  than  on  a  three  per  cent, 
basis. 

Again,  the  three  per  cent,  initial  reserve  in  this 
case  being  the  terminal  reserve  of  the  previous  year 
($410.62,  Verification  Table,  pages  46  and  47),  plus  the 
net  premium  ($47-76),  or  a  total  of  $458.38  on  a  single 
policy,  the  total  reserve  on  609  policies  would  be  $279,- 
153.42,  and  a  gain  from  interest  of  two  per  cent,  would  be 
$5,583.07.  On  the  other  hand,  the  four  per  cent,  initial 
reserve  being  $435.17  on  a  single  policy,  the  total  reserve 
on  609  policies  would  be  $265,018.53,  and  a  gain  from 
interest  of  one  per  cent,  would  be  $2,650.19.  The  saving 
in  mortality  in  the  case  of  the  4  per  cent,  policy  is  the 
greater  by  $41.72,  but  the  gain  from  interest  in  the  case 
of  the  3  per  cent,  policy  is  the  greater  by  $2,932.88. 

Methods  of  Distribution 

The  so-called  "profits"  in  life  insurance — saving 
in  loading,  gain  from  interest,  etc., — are  in  reality 
savings,  not  profits.  Having  assumed  that  our  funds 
would  earn  a  certain  rate  of  interest  and  that  our 
mortality  would  follow  the  table,  the  net  premium  was 
fixed  accordingly.  Subsequent  experience  having  de- 
veloped a  lower  mortality  rate  and  a  higher  rate  of  inter- 
est than  were  assumed,  the  actual  or  net  cost  of  the  insur- 
ance was  found  to  be  less  than  had  been  anticipated. 

106 


The  difference  represents  an  overcharge,  which,  being  re- 
turned to  the  policy-holder,  is  so  much  saved  in  the  cost 
of  his  policy  instead  of  a  profit  earned  on  his  investment. 
Such  savings  are  usually  referred  to  as  Surplus,  being 
funds  received  by  the  company  in  excess  of  what  is  nec- 
essary to  enable  it  to  fulfill  its  contracts.  In  a  stock 
company,  where  such  savings  go  to  the  stockholders 
instead  of  to  the  policy-holders,  they  are,  as  to  the 
former,  genuine  profits. 

In  a  mutual  company,  such  as  The  Mutual  Life, 
the  surplus  or  savings  are  all  returned  to  the  policy- 
holder, the  amount  apportioned  to  each  policy  being 
termed,  somewhat  ineptly,  a  Dividend.  Dividends  may 
be  apportioned  to  policy-holders  yearly  or  at  the  end  of  a 
stated  period  of  years,  as  five,  ten,  fifteen,  twenty,  etc. 
The  former  plan  is  known  as  the  Yearly  Dividend  or 
Annual  Dividend  system,  while  by  the  latter  plan  the 
apportionment  is  made  after  different  methods  variously 
designated  as  Tontine,  Semi-Tontine,  Deferred  Distribu- 
tion, etc.  In  most  companies  the  policy-holder  himself 
elects,  at  the  time  of  making  application,  by  what  system 
his  share  of  the  gains  or  savings  shall  be  apportioned, 
whether  yearly  or  at  the  end  of  a  stipulated  period.  Since 
December  31,  1906,  all  surplus  in  the  case  of  new  issues 
has  been  distributed  by  The  Mutual  Life  yearly. 

Semi-Tontine  Plan 

Under  the  Semi-Tontine  method  of  distribution 
the  policy-holders  are  divided  into  classes,  commonly 
according  to  date  of  entry  and  length  of  distribution 
period  selected.    For  example:  the  members  joining  in  a 

107 


specified  year,  say  1900,  and  selecting  a  particular  distri- 
bution period,  say  fifteen  years,  constitute  a  class  to 
themselves.  All  gains  and  savings  accruing  to  the  policies 
of  this  class  during  the  fifteen  years  are  set  aside  and 
accumulated  to  their  credit.  The  beneficiaries  of  the 
members  who  die  during  the  period  receive  payment  of 
the  face  value  of  their  policies,  and  lapsing  or  withdraw- 
ing members  receive  such  surrender  values  as  may  have 
been  stipulated  in  the  contract  or  required  by  law;  but  in 
either  case,  the  interest  of  such  members  in  the  gains  or 
savings  that  may  have  accrued  up  to  the  date  of  death  or 
withdrawal,  is  forfeited  to  the  remaining  members  of  the 
class,  among  whom  they  are  accordingly  distributed  at  the 
end  of  the  stipulated  period.  Observe  that  Semi-Tontine 
distribution  implies  the  accumulation  of  gains  or  savings 
for  the  benefit  of  a  particular  class,  and  involves  the 
forfeiture  of  the  gains  of  those  members  of  the  class,  who 
die  or  withdraw  during  the  period,  for  the  benefit  of 
those  who  live  or  persist  to  the  end. 

The  Tontine  Method 

Tontine  distribution  differs  from  semi-tontine  in 
that  not  only  the  gains  of  the  lapsing  members  are  for- 
feited, but  their  reserves  as  well.  The  beneficiaries  of 
those  who  die  receive  payment  of  the  face  value  of  their 
policies,  but  those  who  lapse  or  withdraw  before  the  end 
of  the  tontine  period  receive  nothing,  no  surrender  values 
being  allowed.  This  form  of  insurance  is  no  longer 
written  in  this  country,  and  would  in  fact  be  illegal  in 
most  states  under  the  non-forfeiture  laws. 

108 


The  Mutual  Life  Method 

The  method,  which  is  followed  by  The  Mutual 
Life  in  determining  the  dividends  upon  its  policies  issued 
in  former  years  and  having  a  distribution  period  longer 
than  one  year,  differs  essentially  from  the  methods  just 
mentioned.  The  Mutual  Life's  method  is  to  base  these 
long  term  distribution  dividends  upon  the  annual  divi- 
dends which  have  been  declared  each  year  during  the 
distribution  period  in  the  case  of  otherwise  similar  policies, 
which  were  entitled  by  contract  to  receive  dividends 
annually.     The  method  of  calculation  is  as  follows : 

(1)  The  annual  dividends  which  the  policy 
would  have  received  had  it  been  entitled  by  contract  to 
receive  dividends  annually  are  taken:  (2)  these  annual 
dividends  are  accumulated  at  compound  interest  to  the 
end  of  the  distribution  period:  (3)  the  amount  of  these 
accumulated  annual  dividends  is  increased  by  a  percent- 
age as  compensation  for  the  risk  run  of  losing  surplus  by 
death,  discontinuance,  or  otherwise.  In  the  case  of  fifteen 
and  twenty-year  distribution  policies  issued  on  the  1899 
form,  which  guarantee  surrender  values  at  the  end  of  the 
distribution  periods  greater  than  the  reserves  on  similar 
annual  dividend  policies,  the  difference  between  such 
surrender  values  and  such  reserves  is  deducted  from  the 
accumulated  amount  above  described. 

As  is  evident,  this  method  places  the  holders  of 
annual  dividend  policies,  and  the  holders  of  deferred 
distribution  policies  having  different  distribution  periods, 
on  a  perfectly  equitable  basis  as  compared  with  one  an- 
other, as  well  as  with  those  having  policies  with  the 
same  distribution  period. 

109 


The  Contribution  Plan 

The  Contribution  Plan  for  the  apportionment  of 
gains  or  savings  in  life  insurance  was  introduced  in  1863 
by  The  Mutual  Life  Insurance  Company  of  New  York, 
having  been  devised  by  its  then  Actuary,  Mr.  Sheppard 
Homans,  and  his  assistant,  Mr.  David  Parks  Fackler.  It 
has  since  been  adopted  by  American  companies  in  original 
or  modified  form  with  practical  unanimity,  and  by  some 
companies  abroad.  For  annual  dividends  this  method  in 
its  original  form  consists  in  crediting  the  individual 
policy  with  the  reserve  pertaining  thereto  at  the  end  of 
the  previous  year,  and  with  the  annual  premium  paid  at 
the  beginning  of  the  current  year,  less  an  expense  charge, 
adding  interest  at  such  rate  as  the  circumstances  permit. 
Against  the  sum  so  found  are  charged  the  cost  of  insur- 
ance (which  may  or  may  not  be  assessed  according  to  the 
standard  mortality  table),  and  the  reserve  required  at  the 
end  of  the  current  year,  the  balance  being  that  policy's 
"contribution  to  surplus,'*  or  its  annual  dividend. 

Prior  to  the  introduction  of  the  contribution  plan 
by  The  Mutual  Life,  dividends  were  apportioned  in  most 
companies  by  the  Percentage  Method,  the  same  percent- 
age of  the  premium  being  returned  yearly  or  at  the  end 
of  five-year  periods  on  all  policies  alike,  regardless  of 
age  or  form  of  contract  and  often  without  reference  to 
the  length  of  time  the  latter  had  been  in  force.  Methods 
more  or  less  similar  to  that  outlined  were  employed  by 
other  companies. 

Non-Participating  Insurance 
Gains  and  savings  in  life  insurance  are  not  always 
apportioned  to  the  policies  from  whose  premiums  they 

110 


were  derived.  In  some  cases,  in  consideration  of  the 
payment  of  a  smaller  gross  premium,  it  is  agreed  that  the 
policy-holder  shall  receive  no  part  of  the  accruing  surplus 
— that  is,  he  is  to  receive  no  dividends  at  any  time.  The 
policy  in  such  case  is  said  to  be  Non-Participating,  since 
it  is  not  entitled  to  participate  in  distributions  of  surplus. 
On  the  other  hand,  policies  which  are  entitled  to  divi- 
dends are  termed  Participating  contracts.  The  term 
Stock  Rate  is  sometimes  used  as  synonymous  with  non- 
participating. 

Under  the  New  York  law,  no  home  company  can 
write  both  participating  and  non-participating  contracts. 
If  a  mutual  company,  it  can  obviously  write  only  the 
former.  If  a  stock  or  mixed  company,  it  must  choose 
which  form  of  policy  it  will  write,  and  can  then  issue  no 
other,  either  at  home  or  abroad.  Outside  companies 
may  write  only  one  form  within  the  state,  but  may  issue 
either  form  elsewhere. 

Similar  participating  and  non-participating 
policies  having  the  same  reserve  basis,  whether  issued  by 
the  same  or  by  different  companies,  necessarily  have  the 
same  net  premium  and  the  same  reserve  values.  The 
difference  in  gross  rates  is  due  merely  to  a  difference  in 
loading.  The  latter  is  rarely,  if  ever,  sufficient  in  the 
case  of  a  non-participating  policy  to  provide  for  neces- 
sary expenses,  the  purpose  being  to  make  up  the  deficit 
from  the  surplus  accruing  from  other  sources — saving  in 
mortality,  gain  from  interest,  etc.  This  form  of  insur- 
ance is  supposed  to  be  issued  at  as  nearly  net  cost  as 
practicable,  after  providing  for  dividends  to  stockholders. 


Ill 


Life  Insurance  at  Actual  Cost 

If  it  were  certain  that  the  future  death  rate  would 
correspond  precisely  with  the  mortality  table,  and  if  the 
rate  of  interest  to  be  earned  in  the  future  could  be 
determined  in  advance  with  absolute  accuracy,  it  would 
then  be  possible  to  determine  with  certainty  the  exact 
net  premium  which  it  would  be  necessary  to  charge  in 
order  to  furnish  life  insurance  at  actual  cost.  Such 
certainty,  however,  is  impossible.  Omniscience  alone 
can  say  in  advance  what  the  actual  cost  of  life  insurance 
in  the  future  will  be.  If  the  actuary  were  to  undertake 
to  name  a  figure  that  would  precisely  meet  the  case,  he 
would  inevitably  name  a  sum  either  too  large  or  too 
small.  The  latter  alternative  is  not  to  be  contemplated 
for  a  moment.  To  be  on  the  safe  side,  therefore,  it  is 
essential  to  fix  the  premium  at  a  figure  which,  we  are 
morally  certain,  will  prove  to  be  larger  than  actual  cost, 
and  the  margin  over  cost  must,  beyond  a  peradventure, 
be  a  sufficient  margin.  If  that  margin  be  too  small,  un- 
foreseen contingencies  may  wipe  it  out  and  involve  the 
company  in  insolvency  and  ruin.  A  slight  margin  may 
be  safe  enough  if,  by  good  fortune,  all  goes  well.  A 
driver  may  urge  his  team  within  an  inch  of  the  precipice 
and  not  go  over  the  brink,  but  the  prudent  driver  will 
keep  further  back. 

In  other  words,  the  life  insurance  premium,  even 
the  non-participating  premium,  must  be  larger  than 
actual  cost.  That  is  a  condition  which  is  universally 
conceded  to  be  essential.  In  fact,  every  advocate  of 
non-participating   insurance    will   stoutly   maintain   that 

112 


there  is  an  ample  margin  or  overcharge  in  non-participat- 
ing rates.  To  admit  the  contrary  would  be  to  concede 
that  those  rates,  under  adverse  conditions,  might  prove 
too  low  and  thus  involve  the  company  in  ruin. 

What  Becomes  of  the  Over-Charge? 

Although  the  actual  cost  of  life  insurance  cannot 
be  determined  in  advance,  it  can  be  computed  at  the 
end  of  each  year  when  the  books  are  balanced.  The 
mutual  company — that  is,  a  company  writing  participat- 
ing insurance — ^will  then  return  the  over-charge  to  the. 
policy-holder  in  the  form  of  a  so-called  dividend.  Thus 
from  year  to  year  the  insured  does,  by  the  participating 
plan,  obtain  his  insurance  at  actual  cost.  In  the  case  of 
the  stock  company  which  writes  only  non-participating 
policies,  the  over-charge,  or  margin  over  actual  cost,  goes 
to  the  stockholders.  Nothing  is  returned  to  the  policy- 
holder in  any  event.  The  cost  to  him  is  absolutely  fixed. 
He  knows  in  advance  "just  what  he  is  to  pay,**  and  he 
knows,  too,  that  he  will  get  nothing  back. 

Let  us  not  complicate  this  question  by  discussing 
the  merits  of  different  companies,  or  the  varying  condi- 
tions under  which  they  operate.  To  decide  whether  the 
participating  or  non-participating  system  is  correct,  we 
must  assume  in  advance  that  the  two  companies  are  man- 
aged with  equal  honesty  and  efficiency,  and  that  attendant 
conditions  are  substantially  the  same.  It  then  follows, 
as  certainly  as  two  and  two  are  four,  that  only  in  partici- 
pating insurance  is  protection  at  actual  cost  a  possibility. 

The  advocate  of  the  non-participating  plan  will 
claim  that,  while  his  premium  does  include  an  over-charge 

118 


as  a  provision  for  stockholders*  profits  and  as  a  margin 
of  safety,  the  participating  premium  carries  a  larger 
margin  than  is  necessary.  This  may  sometimes  be  true, 
but  inasmuch  as  that  difficulty  is  adjusted  at  the  end  of 
each  year,  when  the  books  are  balanced  and  the  over- 
charge returned,  the  policy-holder  will  be  content  to  have 
it  so,  since  the  larger  margin  affords  greater  assurance  of 
safety.  No  one  can  tell  what  the  exigencies  of  the  future 
may  develop.  Adverse  legislation,  excessive  taxation, 
other  imforeseen  contingencies,  such  as  would  wipe  out 
the  margin  in  the  non-participating  premium  and  en- 
danger the  solvency  of  the  company,  would  result  only  in 
a  diminution  of  dividends  in  case  of  a  mutual  company 
with  its  larger  participating  premiums.  Safety  is  of 
more  importance  in  life  insurance  than  all  else.  It  is 
better  to  keep  away  from  the  brink  of  the  precipice,  even 
at  some  temporary  inconvenience. 

Within  the  last  ten  years,  many  new  companies 
have  been  organized.  A  number  of  these  institutions 
have  very  limited  resources — are  in  fact  still  in  the  ex- 
perimental stage — ^and  some  are  directed  by  men  who, 
however  successful  they  may  have  been  as  insurance 
agents,  have  had  little  or  no  experience  in  company 
management.  A  large  number  of  these  organizations 
write  participating  insurance  with  a  sufficient  margin  in 
their  premiums  to  enable  them  to  survive  the  mistakes 
commonly  incidental  to  the  inexperience  and  over-confi- 
dence of  youth.  Others  propose  to  write  non-participating 
insurance  exclusively,  thereby  taking  chances  that  com- 
panies long  established  and  of  great  strength  might  well 
hesitate  to  assume.     The  company  that  essays  to  write 

114 


this  class  of  business,  not  having  the  reserve  strength 
afforded  by  the  redundant  premiums  of  participating 
insurance,  should  at  least  possess  large  capital  as  a 
guaranty  against  possible  disaster  from  the  use  of  rates 
that  may,  under  adverse  conditions,  prove  insufficient. 


116 


CHAPTER  X 

Natural  Premium  Insurance 

ATl/E  have  seen  that  the  net  annual  premium  of  an 
ordinary  life  policy  at  age  fifty-six  based  on  the 
American  Experience  Table  of  Mortality  and  three  per 
cent,  interest^  is  $47-76,  or  more  accurately,  $47.760895. 
This  is  the  net  amount  mathematically  necessary  to  be 
paid  yearly  during  life  by  each  of  the  63,S64i  members  of 
our  hypothetical  company,  to  make  possible  the  payment 
of  $1,000  for  each  death  until  the  last  three  members 
pass  away  at  age  ninety-six.  By  reference  to  the  Verifi- 
cation Table,  pages  46  and  47,  it  will  be  seen  that  this 
amount  paid  by  each  of  the  63,364  members,  yields  in  the 
first  year  the  sum  of  $3,026,321.35,  while  the  death  claims 
to  be  met  in  that  year  are  only  $1,260,000.  We  have 
therefore  collected  much  more  than  was  necessary  for  the 
payment  of  current  claims,  but  it  has  been  proved  in  the 
Verification  Table  that  the  excess  collected  in  the  earlier 
years  will  all  be  needed  at  a  later  period,  when  the 
members  are  older  and  the  death  rate  higher.  It  is 
obvious,  therefore,  that  if  we  were  to  collect  only  enough 
in  any  year  to  pay  the  death  claims  of  that  year,  we 
should  have  to  charge  a  continually  increasing  premium 
in  subsequent  years. 

To  illustrate:  Of  the  63,364  persons  at  age 
fifty-six  comprising  our  hypothetical  company,  1,260, 
according  to  the  Mortality  Table,  will  be  dead  at  the  end 
of  the  year,  requiring  a  payment  at  that  time  of 
$1,260,000.  To  provide  for  this  amount  we  shall  have  to 
collect  from  the  members  at  the  beginning  of  the  year  a 

116 


premium  sufficient  to  amount  in  the  aggregate  to  the  pres- 
sent  worth  of  that  sum ;  that  is^  a  fund  which  at  three  per 
cent,  interest  will  amount  to  $1,260,000  at  the  end  of  the 
year.  The  present  worth  of  $1.00  due  in  one  year  is 
$0.97087379.  Hence  the  present  worth  of  $1,260,000  is 
$1,223,300.98.  ($0.97087379  x  1,260,000  =  $1,223,- 
300.98).  Dividing  this  amount  by  63,364,  the  number  of 
members  living  at  the  beginning  of  the  year,  we  get 
$19.31.  That  is  to  say,  if  each  member  at  the  beginning 
of  the  year  will  pay  a  net  premium  of  $19.31,  or,  more 
accurately,  $19.3059305,  we  shall  have  a  total  insurance 
fund  of  $1,223,300.98,  which  at  three  per  cent,  interest 
will  amount  to  $1,260,000  at  the  end  of  the  year,  or  just 
enough  for  the  payment  of  the  accrued  claims. 

At  the  beginning  of  the  second  year  we  have 
62,104  members  still  living  of  whom  1,325  will  be  dead 
at  the  end  of  year^  requiring  the  payment  at  that  time  of 
$1,325,000.  The  present  worth  of  this  sum  due  in  one 
year  is  $1,286,407-77,  which  is  therefore  the  amount  to 
be  collected  at  the  beginning  of  the  year.  Dividing  by 
62,104  we  get  $20.71,  which  is  the  net  premium  to  be 
paid  by  each  member  in  the  second  year.  By  like  process 
we  find  that  the  net  premium  for  the  third  year  at  age 
fifty-eight  is  $22.27. 

The  premium  thus  determined  is  called  the 
Natural  Premium  as  distinguished  from  the  Level 
Premium,  with  which  we  have  heretofore  had  to  do,  the 
latter  being  a  fixed  charge  that  can  never  be  increased, 
and  which  is  sufficient  both  for  current  and  future  cost. 
The  Natural  Premium  represents  the  actual  current  cost 
and  increases  each  year  as  the  insured  advances  in  age, 

117 


and  in  proportion  to  the  probability  of  his  dying.  This 
form  of  insurance  as  in  use  with  the  fraternal  orders  is 
sometimes  called  the  Step-Rate  plan,  and  is  the  same  as 
yearly  renewable  term  insurance  heretofore  described. 

The  natural  premium  does  not  increase  rapidly  at 
the  younger  ages,  but  advances  at  a  vastly  greater  rate  as 
the  insured  approaches  the  limit  of  life,  as  will  be  seen  by 
the  following  table. 

Age  Natural  Prem.  Age  Natural  Pretn 

35. $8.69  60 $25.92 

36 8.82  70 60.19 

87 8.97  80 140.26 

40 9.51  90 441.31 

50 13.38  95 970.87 

The  Cost  op  New  Business 

One  of  the  principal  items  of  expense  with  a  life 
insurance  company  is  the  cost  of  new  business.  Ordi- 
narily, the  agent  who  places  a  policy  receives  a  Com- 
mission for  his  services,  which  may  be  a  percentage  of  the 
first  premium  only,  termed  a  Brokerage,  or  it  may  include 
B  smaller  percentage  of  a  stated  number  of  subsequent 
premiums,  termed  a  Renewal  Commission.  Although  the 
renewal  commission  is  a  percentage  of  subsequent  prem- 
iums, a  part  of  it,  at  least,  should  be  included  in  the  cost 
of  new  business.  This  is  clear  from  the  fact  that  the 
agent  is  induced  to  accept  a  smaller  brokerage,  or  per- 
centage of  the  first  premium,  by  the  offer  of  a  sub- 
stantial renewal.  Moreover,  it  is  often  the  case  that 
the  agent  receiving  the  renewal  commission  has  noth- 
ing whatever  to  do  with  the  collection  of  subsequent 
premiums,  the  contract  even  providing  in  some  cases  for 

118 


the  continuance  of  renewals  after  the  death  of  the  agent, 
or  after  the  termination  of  his  connection  with  the 
company. 

There  are  other  matters  of  expense  pertaining 
partly  to  the  cost  of  new  insurance,  partly  to  the  care  of 
old  business,  which  it  would  be  equally  impracticable  to 
apportion  with  entire  accuracy  between  the  two  items. 
However,  the  New  York  law,  for  the  purpose  of  placing 
a  limit  upon  expenses,  designates  the  items  which  shall  be 
considered  as  constituting  the  cost  of  new  business,  but 
without  assuming  scientific  accuracy. 

The  Preliminary  Term  System, 

The  statement  may  be  safely  made  that  the  ordi- 
nary loading  of  a  life  insurance  premium  is  never  suffi- 
cient in  the  first  year  to  meet  the  expenses  incident  to 
securing  the  business.  To  illustrate:  If  the  gross  premium 
of  an  ordinary  life  policy  at  age  fifty-six,  American 
Experience  Table  and  three  per  cent,  interest,  is  $63.68, 
we  find,  by  deducting  the  net  premium  of  $47.76,  that 
the  loading  is  $15.92.  The  principal  items  of  expense 
the  first  year  will  be  the  agent's  commission,  say  forty 
per  cent.,  or  $25.47,  and  the  medical  examiner's  fee, 
$5.00,  making  for  these  two  items  alone  $30.47,  or  nearly 
double  the  amount  of  the  loading  earned  by  the  new 
policy.  Inasmuch  as  the  agent,  when  settling  for  prem- 
iums collected,  usually  retains  his  commission,  remitting 
only  the  net  amount,  the  erroneous  impression  has  gained 
acceptance  that  the  commission  is  paid  from  the  first 
premium.    As  a  matter  of  fact,  the  commission  and  other 

119 


cost  of  new  business  are  paid  from  the  entire  loadings 
of  the  company,  earned  on  all  policies  outstanding, 
or  from  other  funds  available  for  expenses.  The  com- 
mission could  not  be  paid  from  the  first  premium, 
for  the  net  premium,  or  reserve,  must  not  be  trenched 
upon,  as  would  occur  in  that  case.  Neither  is  the  re- 
quired amount  "borrowed"  from  the  "surplus  belonging 
to  old  policy-holders,"  as  so  often  stated.  The  loadings 
of  all  policies  in  force  are  for  expenses,  including  the 
cost  of  new  business. 

In  the  case  of  young  companies,  however,  which 
have  but  little  insurance  in  force  and  hence  small  receipts 
from  loading,  the  policy  sometimes  provides  that  the  con- 
tract shall  be  valued  in  the  first  year  as  term  insurance, 
the  regular  life  insurance  policy  beginning  one  year  later. 
Thus  the  entire  first  premium,  less  only  the  charge  for 
the  actual  mortality  of  the  year,  is  available  as  a  loading 
for  meeting  the  cost  of  new  business.  This  method  is 
variously  designated  as  the  Preliminary  Term,  or  First 
Year  Term,  system,  and  has  been  adopted  by  most  com- 
panies organized  in  recent  years.  In  the  case  of  a  pre- 
liminary term  ordinary  life  policy  at  age  fifty-six,  the 
net  premium  in  the  first  year  would  be  merely  the  natural 
premium,  or  yearly  term  rate,  that  is,  $19.31,  as  given 
above  (page  117).  The  practice  of  preliminary  term 
companies  is,  however,  to  charge  the  same  gross  premium 
in  the  first  as  in  subsequent  years.  If  the  gross  premium 
is  $63.68,  we  shall  have,  after  deducting  the  net  premium 
of  $19.31,  a  loading  the  first  year  of  $44.37,  or  about 
seventy  per  cent.  Deducting  $5.00  for  medical  examina- 
tion, there  remains  a  balance  of  $39.37,  or  nearly  sixty- 
two  per  cent.,  for  commissions  and  other  expenses. 

120 


In  the  valuation  of  such  a  contract  the  company 
is  not,  of  course,  charged  with  any  reserve  at  the  end  of 
the  first  year,  but  during  the  second  and  subsequent  years 
the  net  premium  required  will  be  that  of  an  ordinary  life 
corresponding  to  age  fifty-seven,  the  attained  age  of  the 
insured  when  the  regular  life  policy  begins.  In  this 
case,  then,  the  net  premium  in  the  second  and  subsequent 
years  would  be  $50.13  instead  of  $47-76  (the  net  premium 
at  age  56),  and  if  this  amount  be  deducted  from  the 
gross  premium  of  $63.68,  the  balance  of  $13.55  will  be 
the  permanent  loading  instead  of  $15.92.  Thus  it  will 
be  seen  that  by  this  system  the  loading  is  greatly  increased 
in  the  first  year,  but  is  materially  less  than  the  regular 
loading  in  subsequent  years.  There  will  be  no  reserve 
at  the  end  of  the  first  year,  and  the  reserve  of  the  second 
policy-year  will  be  the  same  as  the  first  year  reserve  of  a 
regular  ordinary  life  policy  issued  at  age  fifty-seven.  In 
fact,  from  the  beginning  of  the  second  year  the  policy 
will  be  valued  as  an  ordinary  life  issued  at  age  fifty-seven, 
or  one  year  later  than  its  actual  date,  as  stated  above.  It 
follows  that  the  accumulated  reserve  of  an  ordinary  life 
policy  issued  on  the  preliminary  term  plan  will  at  all 
stages  be  less  than  it  would  have  been  had  it  been  issued 
at  the  same  age  on  the  regular  ordinary  life  plan,  because 
always  one  year  behind  in  the  process  of  accumulation. 
This  difference  will  continue  until  age  ninety-six,  when 
the  reserve  in  either  case  becomes  equal  to  the  face  of  the 
policy.  It  will  be  appreciated  that  smaller  reserves  mean 
smaller  cash  values,  and  also  that  smaller  loadings  mean 
smaller  dividends. 

We  have  heretofore  defined  the  terms  "level 
premium"  and  "net  valuation."     Under  the  preliminary 

181 


term  system  the  gross  premium  may  be  level  from  date 
of  issue  of  policy,  but  the  net  premium  is  not  so.  For 
example,  in  the  case  just  illustrated,  the  net  premium  in 
the  first  year  is  $19.31  and  in  subsequent  years  $50.13, 
although  the  gross  premium  is  $63.68  for  every  year.  On 
the  other  hand,  we  have  seen  that  the  net  premium  of 
the  equivalent  ordinary  life  policy  on  the  regular  legal 
reserve  plan  is  $47.76,  the  same  fixed  amount  for  every 
year  including  the  first.  In  that  case  we  have  a  Level 
Net  Premium  as  distinguished  from  the  net  premium  of 
the  preliminary  term  plan,  which  is  not  level. 

In  the  case  of  a  "limited  premium"  policy  the 
preliminary  term  plan  varies  somewhat  from  that  illus- 
trated. Let  us  consider  its  application,  for  example,  to 
a  fifteen  payment  life.  The  net  three  per  cent,  premium 
of  the  regular  policy  at  age  fifty-six  would  be  $60.17. 
If  the  gross  premium  is  $78.16,  the  yearly  loading  will 
be  $17.99.  On  a  preliminary  term  basis,  the  equivalent 
contract  would  consist  of  a  combined  one  year  term  policy 
and  a  fourteen  payment  life,  the  latter  beginning  at  age 
fifty-seven.  The  net  premium  for  one  year's  term  insur- 
ance would  be  the  same  as  before,  $19.31.  Deduct- 
ing this  amount  from  the  gross  premium  of  $78.16, 
we  obtain  a  first  year  loading  of  $58.85.  The  three  per 
cent,  net  premium  of  the  fourteen  payment  life  at  age 
fifty-seven  would  be  $64.55,  which  leaves  a  yearly  loading 
of  $13.61,  instead  of  $17.99,  for  the  remaining  fourteen 
years.  As  in  the  case  of  the  preliminary  term  ordinary 
life,  there  will  be  no  reserve  at  the  end  of  the  first  year. 
At  the  end  of  the  second  policy  year  the  reserve  will  be 
,14.     This  is  larger  than  the  first  year  reserve  of  the  _^ 

122 


regular  policy^  but  much  smaller  than  the  reserve  of  the 
latter  at  the  end  of  the  second  policy  year^  it  being  then 
$86.72.  The  preliminary  term  reserve  at  the  end  of 
each  subsequent  policy  year  approaches  more  and  more 
nearly  to  the  corresponding  reserve  of  the  regular  fifteen 
payment  life  until  the  end  of  the  fifteenth  year  when,  at 
the  attained  age  of  seventy-one,  both  reserves  are  neces- 
sarily the  same,  since  both  policies  are  now  fully  paid  up. 
In  other  words,  on  the  regular  fifteen  payment  life  the 
reserve  of  a  fully  paid  policy  is  accumulated  in  fifteen 
years,  while  on  the  preliminary  term  fifteen  payment  life 
the  same  reserve  is  accumulated  during  the  last  fourteen 
years. 

The  preliminary  term  system,  as  applied  to  an 
ordinary  life  policy,  is  not  an  unreasonable  method  of 
providing  for  the  cost  of  new  business  in  the  case  of  a 
young  company,  notwithstanding  the  apparent  injustice 
of  charging  a  premium  of  $63.68  for  term  insurance 
during  a  single  year,  the  net  natural  cost  of  which  is 
$19.31.  Indeed,  only  by  the  use  of  some  such  expedient 
would  it  be  possible  for  a  new  company  to  establish  itself 
at  all  on  the  mutual  plan,  since,  being  in  receipt  of  little 
or  nothing  from  loadings  on  old  business  and  having  no 
accumulated  surplus,  it  would  be  unable  to  meet  the 
necessary  cost  of  new  insurance  and  provide  at  the  same 
time  for  the  required  legal  reserve  of  the  first  year. 
Only  on  the  stock  plan,  with  the  stockholders  personally 
advancing  extra  funds  for  the  purchase  of  new  business, 
could  a  new  company  comply  with  the  requirement  to 
put  up  the  full  level  net  premium  reserves  on  its  policies 
beginning  with  the  year  of  issue.     The  adoption  of  the 

128 


preliminary  term  plan  by  an  old  company,  however,  is 
commonly  regarded  as  a  confession  of  weakness  or  of  an 
extravagant  management,  since  it  is  a  virtual  admission 
that  the  company  is  unable  to  keep  its  expenses  within 
its  aggregate  receipts  from  loadings  on  all  business,  and 
that  it  dare  not  trench  upon  its  limited  surplus. 

If  the  application  of  the  preliminary  term  plan  to 
the  ordinary  life  policy  is  defensible,  it  nevertheless 
becomes  decidedly  objectionable  when  applied  without 
modification  to  limited  payment  and  endowment  policies, 
as  illustrated  in  the  following  table  showing  the  loadings 
of  the  first  year: 

Policy.  Age  56  p,^^^^^^         Natuml'cost         ^^^^ding 

Ordinary   Life $63.68  $19.31  $44.37 

Fifteen  Payment  Life....      78.16  19.31  58.85 

Ten  Payment  Life 99.33  19.31  80.02 

Twenty  Year  Endowment.     72.66  19.31  53.35 

Ten  Year  Endowment 121.06  19.31  101.75 

The  grotesque  absurdity  of  such  loadings,  suffi- 
ciently condemns  the  Full  Preliminary  Term  system, 
by  which  is  meant  the  application  of  preliminary  term 
without  modification  to  all  forms  of  policies. 

Modified  Preliminary  Term 

In  1897  there  was  introduced  a  modification  of 
the  preliminary  term  plan,  which  consisted  in  limiting  the 
loading  of  the   first  year   on   all  limited   payment  and 

124 


endowment  forms  to  the  amount  available,  on  a  prelimi- 
nary term  basis,  on  the  ordinary  life  policy.  For  ex- 
ample, referring  to  the  table  above,  while  the  gross 
premiums  would  vary  on  the  different  forms  as  indicated, 
the  loading  could  in  no  case  exceed  that  of  the  ordi- 
nary life  policy,  to  wit:  $44.37.  From  the  balance 
of  the  premium  on  limited  payment  and  endowment 
forms  the  company  would  put  up  a  reserve  in  the 
first  year,  thus  reducing  the  net  premium  and  in- 
creasing the  loadings  of  subsequent  years.  The 
tendency  of  this  plan  would  be  to  encourage  the  sale  of 
ordinary  life  policies  rather  than  limited  payment  and 
endowment  contracts.  Several  modifications  of  "modified 
preliminary  term"  have  been  legalized  in  different  states. 

Select  and  Ultimate  Valuation 

This  method  of  computing  reserves  was  devised 
as  a  substitute  for  modified  preliminary  term.  To  a 
correct  understanding  of  the  system  a  knowledge  of  the 
several  classes  of  mortality  tables  is  necessary. 

Assume,  for  illustration,  that  we  wish  to  ascertain 
how  many  of  100,000  persons,  all  thirty  years  of  age, 
will  die  within  one  year.  If  to  that  end  we  note  the 
history  for  twelve  months  of  100,000  persons  of  the  age 
stated,  who  have  just  passed  a  rigid  medical  examination 
for  life  insurance,  we  shall  find  a  much  smaller  number 
dying  than  in  100,000  of  the  same  age  who  were  examined 
five  years  ago,  at  age  twenty-five.  If  we  note  the  history 
of  both  classes  during  the  succeeding  year,  we  shall  find 
a  larger  percentage  of  deaths  in  each  instance  than  in  the 
first  year,  and,  as  before,  a  smaller  percentage  of  deaths 

125 


in  the  first  than  in  the  second  class,  but  the  death  rates 
of  the  two  classes  will  now  be  nearer  together  than  in 
the  first  year.  In  the  third  year,  while  the  death  rate  of 
each  class  will  again  be  higher  than  formerly,  the  differ- 
ence between  the  two  rates  will  again  be  less  than  in  the 
second  year.  With  each  added  year  the  difference  in 
death  rates  of  the  two  classes  will  diminish,  until  ulti- 
mately, after  the  benefit  of  medical  selection  has  worn 
off,  the  two  death  rates  will  be  theoretically  the  same. 
It  is  commonly  assumed  that  this  stage  will  be  reached 
in  five  years. 

Lives  which  have  just  been  selected  by  a  medical 
examination  are  called  Select  Lives,  and  a  mortality 
table  based  on  the  subsequent  history  of  such  lives  is 
called  a  Select  Table, 

As  it  is  assumed  that  the  effects  of  medical 
selection  ultimately  disappear,  say  in  about  five  years,  a 
mortality  table  based  on  the  history  of  lives  insured  five 
or  more  years  before  is  called  an  Ultimate  Table. 

A  mortality  table  based  on  the  history  of  lives 
insured,  some  within  the  year,  others  within  two  or  three 
or  ten  years  or  more,  is  called  a  Mixed  Table, 

The  American  Experience  Table  of  Mortality, 
which  is  in  general  use  in  the  United  States,  is  an 
"ultimate  table,"  its  compilation  having  been  based 
upon  the  subsequent  history  of  lives  insured  for  five 
years  or  more.  The  rate  of  mortality  indicated  by  this 
table,  therefore,  is  materially  greater  in  the  first  five 
years,  at  least,  than  that  pertaining  to  select  lives  at 
corresponding  ages.  As  a  basis  for  establishing  a  mini- 
mum standard  of  valuation  and  for  fixing  a  limitation  of 

128 


expenses  in  securing  new  business,  the  New  York  Law 
assumes  that  the  mortality  of  select  lives  in  the  first 
policy-year  immediately  following  medical  examination 
will  be  fifty  per  cent,  of  the  tabular  mortality  of  the 
American  Experience  Table ;  in  the  second  year,  sixty-five 
per  cent. ;  in  the  third  year,  seventy-five  per  cent. ;  in  the 
fourth  year,  eighty-five  per  cent. ;  in  the  fifth  year,  ninety- 
five  per  cent. ;  and  in  the  sixth  and  subsequent  years,  one 
hundred  per  cent.  On  ihis  basis  smaller  terminal  reserves 
will  be  required  during  the  first  four  years  than  by  the 
American  Experience  Table  though  they  will  be  the 
same  from  the  fifth  year  on,  as  illustrated  in  the  follow- 
ing comparison  of  terminal  reserves  computed  by  the  two 
methods  on  an  ordinary  life  policy  issued  at  age  fifty-six. 

End  of 
Year 

First 

Second 

Third 

Fourth 

Fifth 

Sixth 

This  is  the  system  of  Select  and  Ultimate  Valu- 
ation authorized  by  the  laws  of  New  York  as  a  minimum 
standard.  In  this  standard  the  new  company,  which 
might  find  it  impracticable  to  put  up  the  level  net  pre- 
mium reserves  in  the  first  and  immediately  succeeding 
years,  has  a  substantial  measure  of  relief.  The  company 
collects  during  the  first  four  years,  as  well  as  thereafter, 
the  full  gross  premium.     The  margin  in  the  first  year's 

137 


Terminal  Reserves 
American   Kx-            Select  and 
perience  Table             Ultimate 

$29.90 

$14.41 

59.94 

,  50.84 

90.06 

85.87 

120.21 

119.13 

150.33 

150.33 

180.36 

180.36 

premium  by  reason  of  the  smaller  reserve  required — the 
full  reserve  being  made  up  in  subsequent  years  by  the 
saving  in  mortality — is  available  for  other  purposes  and 
may  be  anticipated  and  expended  in  securing  new 
business. 


chapter  xi 
Sundry  Topics 

T  N  the  foregoing  pages  we  have  discussed  in  their  logi- 
■*■  cal  order  such  technical  subjects  and  defined  such 
terms  as  seemed  important  for  the  life  insurance  agent  to 
understand.  The  items  treated  of  may  well  be  supple- 
mented by  a  few  others,  heretofore  omitted  because  not 
necessary  to  the  proper  comprehension  of  the  current  text. 

Insurable  Interest 

The  question  of  insurable  interest  is  frequently  an 
important  one.  Since,  however,  the  law  on  this  subject 
varies  so  much  in  the  different  states,  it  is  impossible  to 
make  a  satisfactory  general  statement  of  the  law  relating 
to  it.  In  some  of  the  states  (for  instance.  New  York),  a 
very  liberal  view  obtains,  and  it  is  held  that  where  the 
person  whose  life  is  insured  makes  application  for  the 
insurance  he  can  name  any  person  as  the  beneficiary,  and 
that  in  such  a  case  it  is  not  necessary  to  inquire  whether 
the  proposed  beneficiary  has  an  insurable  interest  in  the 
life  of  the  insured  or  not.  In  other  states  it  is  necessary 
in  all  cases  to  inquire  whether  the  proposed  beneficiary 
has  such  a  pecuniary  interest  in  the  life  of  the  insured  as 
would  permit  him,  the  beneficiary,  to  apply  for  and 
obtain  insurance  upon  the  life  of  the  insured.  In  the 
case  of  certain  near  relationships  such  as  husband  and 
wife,  parent  and  child,  an  insurable  interest  is  pre- 
sumed.    In  some  states,  however,  an  adult  child  is  held 

129 


not  to  have  an  insurable  interest  in  the  life  of  his  parent 
unless  the  child  is  actually  dependent  upon  the  parent 
for  his  support. 

It  is  quite  generally  held  that  a  creditor  has  an 
insurable  interest  in  the  life  of  his  debtor  to  the  extent 
of  his  debt;  also  that  one  partner  has  an  insurable  in- 
terest in  the  life  of  another  partner. 

The  question  of  insurable  interest  also  arises  in 
connection  with  assignments  of  life  insurance  policies. 
Some  states,  including  New  York,  take  the  liberal  view 
that  an  assignee  need  have  no  insurable  interest  in  the 
life  of  the  insured  unless  it  appears  that  the  assignment 
is  made  for  the  express  purpose  of  speculating  on  the 
life  of  the  insured.  In  other  states  the  assignee  is 
required  to  have  an  actual  pecuniary  interest  in  the  life 
of  the  insured;  that  is,  the  assignee  must  sustain  such 
relation  to  the  insured  that  the  death  of  the  latter  would 
cause  a  pecuniary  loss  to  the  assignee. 

Standard  Policies 

All  policies  issued  in  New  York  State  by  New 
companies  must  include  the  "standard  provisions"  pre- 
scribed by  the  New  York  Laws.  New  forms  of  policies 
may  be  issued  when  approved  by  the  insurance  depart- 
ment after  a  public  hearing  open  to  all  persons  interested. 
The  approved  forms  then  become  **standard"  and  may  be 
written  by  any  company. 

Annuities 
In  addition  to  the  life  annuity  (page  20)  and  the 
temporary  annuity  (page  31),  several  other  forms  require 
our  attention. 

130 


A  Survivorship  Annuity  is  one  which  becomes 
payable  to  a  designated  person,  beginning  at  the  death  of 
the  insured.  This  contract,  as  written  by  The  Mutual 
Life,  enables  the  insured  to  provide  a  life  income  for  a 
designated  beneficiary,  an  aged  parent  for  example,  at  a 
much  smaller  outlay  than  by  any  other  form. 

A  Deferred  Annuity  is  one,  the  payments  of 
which  do  not  begin  until  a  specified  future  date,  or  the 
occurrence  of  a  designated  future  event.  This  contract 
enables  the  insured,  who  may  have  no  one  dependent 
upon  him,  to  provide  an  income  for  his  own  old  age  at  a 
smaller  outlay  than  by  any  other  method. 

When  an  annuity  is  to  be  paid  for  a  specified 
number  of  years,  no  more  and  no  less,  as  ten  or  twenty, 
whether  the  annuitant  continues  to  live  or  not,  and  re- 
gardless of  any  other  contingencies,  we  have  an  Annuity 
Certain.  If  the  proceeds  of  a  policy,  for  instance,  are  to 
be  paid  in  a  fixed  number  of  yearly  instalments  of  a 
stated  amount  each,  such  instalments  constitute  an 
annuity  certain.  The  present  worth  of  such  instalments, 
that  is,  the  sum  in  hand  which,  at  a  given  rate  of  interest, 
will  produce  instalments  of  thd  stated  number  and 
amount,  is  termed  the  Commuted  Value  thereof,  and  is, 
of  course,  also  the  value  of  the  annuity  in  that  case. 

A  Perpetual  Annuity  is  one  which  is  to  be  paid 
continuously,  without  limit  of  duration.  Such  annuities 
are,  perhaps,  unknown  in  this  country,  but  are  common 
in  England,  Corporation  shares  or  bonds  which  are 
never  to  be  redeemed,  but  which  bear  a  specified  rate  of 
interest  in  perpetuity,  come  within  this  designation,  the 
interest  payments  constituting  a  perpetual  annuity.  The 
British  consol  is  an  example  of  a  perpetual  annuity. 

181 


Neither  the  annuity  certain  nor  the  perpetual 
annuity  involves  any  question  of  Life  Contingency;  that 
is  to  say,  they  are  not  based  upon  the  probability  of  the 
continuance  or  termination  of  a  designated  life,  and  life 
insurance  companies  accordingly  do  not  issue  such 
contracts,  save  annuities  certain  as  supplementary  to  in- 
surance policies. 

All  Nevr  York  standard  policies  of  the  ordinary 
life,  limited  payment  life,  term  or  endowment  forms, 
may,  at  the  election  of  the  insured,  (or  at  the  election  of 
the  beneficiary  if  the  insured  has  not  acted  in  his  life- 
time), be  made  payable  either  in  a  specified  number  of 
equal  yearly  instalments,  as  an  annuity  certain,  or  as  a 
Continuous  Intalment  Policy.  The  latter  plan  involves 
two  forms  of  annuity,  to  wit:  An  annuity  certain  and  a 
deferred  survivorship  annuity.  To  illustrate:  Upon  the 
death  of  the  insured,  an  annuity  contract  will  be  issued 
providing,  first:  for  the  payment  of  annual  instalments 
of  an  amount  stated  in  the  policy  for  twenty  years 
certain,  and  second:  for  the  continuation  to  the  bene- 
ficiary of  this  annuity  as  long  as  she  may  live  beyond  the 
twenty  years  certain.  When  this  form  of  settlement  is 
applied  to  policies  which  by  their  terms  are  payable  in  a 
single  sum,  the  ampunt  of  each  instalment,  or  the  annuity, 
depends  upon  the  age  of  the  beneficiary  when  the  policy 
becomes  payable.  Any  policy  on  the  books  of  the  Com- 
pany, which  is  payable  in  a  single  sum  of  not  less  than 
$1,000,  may  be  settled  in  this  manner,  no  matter  how 
long  ago  issued,  unless  there  are  legal  difficulties  in  the 
way.  The  regular  continuous  instalment  policy,  in  its 
original  form,  provides  by  its  terms  for  payment  to  a 

182 


designated  beneficiary  in  yearly  or  monthly  instalments. 
It  differs  from  the  mode  of  settlement  first  described  in 
that  each  instalment  is  for  a  specified  sum  fixed  at  time 
of  issue,  the  unit  being  $50  yearly  or  $10  monthly.  The 
amount  of  the  premium  in  this  form  is  determined  ac- 
cording to  the  age  of  both  the  insured  and  the  bene- 
ficiary at  date  of  issue.  The  continuous  instalment  con- 
tract is  the  ideal  policy  for  the  average  family,  pro- 
viding, as  it  does,  without  danger  of  loss  and  without 
care  of  investment,  an  absolute  income  for  a  period  of 
twenty  years,  whether  the  beneficiary  lives  so  long  or  not, 
within  which  time  the  youngest  child  becomes  self-sup- 
porting, and  provides  further  for  a  continuance  of  the 
income  during  the  lifetime  of  the  beneficiary,  if  the  latter 
survives  the  period  named.  The  policy  is  now  written 
by  most  companies  under  one  name  or  another,  but, 
in  its  original  form,  was  devised  in  1892  by  Emory 
McClintock,  then  and  for  many  years  the  renowned 
actuary  of  The  Mutual  Life  Insurance  Company  of  New 
York,  and  was  introduced  by  that  Company  in  its  cen- 
tennial year,  1893. 

Within  the  last  three  or  four  years,  numerous 
assessment  companies  have  been  organized  to  write  a 
somewhat  similar  contract,  sometimes  with  the  additional 
provision  that  the  annuity  in  case  of  a  widow  shall  termi- 
nate upon  the  remarriage  of  the  latter.  Their  rates,  not 
being  scientifically  computed,  are  absurdly  inadequate; 
the  annuity  payments  are  in  all  cases  for  the  same 
amount  per  $1,000.00  of  insurance,  regardless  of  the  at- 
tained or  previous  age  of  the  annuitant;  and  the  contract 
docs  not  contemplate  the  accumulation  of  a  mathematical 
reserve.  Furthermore,  the  contingency  of  marriage,  like 
that  of  lapse,  cannot  well  be  considered  in  the  computa- 
tion of  the  premium.  The  law  of  probabilities  cannot  be 
applied  satisfactorily  to  an  event  which,  like  that  of  lapse 


or  marriage,  is  largely  or  wholly  within  the  control  of  the 
party  most  concerned.  It  is  a  different  question  from 
the  application  of  the  law  to  events  which,  like  death, 
sickness  or  accident,  are  wholly  fortuitous. 

A  Contingent  Annuity  is  one  which  is  to  terminate 
on  the  happening  of  a  stated  future  event,  as  the  death 
of  a  designated  person  other  than  the  annuitant,  the 
marriage  of  the  annuitant,  the  inheritance  of  an  estate, 
etc.  The  specified  event  may  be  one  which  is  bound  to 
occur,  as  in  the  first-mentioned  case,  or  one  which  may 
never  take  place,  as  in  the  last  instance.  It  is  possible, 
therefore,  that  a  contingent  annuity  may  prove  to  be 
perpetual,  as  it  might,  for  instance,  when  payable  during 
the  life  of  the  annuitant  and  thereafter  to  his  next  of 
kin.  The  extinction  of  his  line  would  terminate  the 
annuity,  but  this  event  may  never  occur.  The  contingent 
annuity  is  not  written  by  The  Mutual  Life,  nor,  probably, 
by  many  American  legal  reserve  companies,  if  any. 

A  Joint  Annuity  is  one  in  which  two  or  more  lives 
participate  and  which  is  to  terminate  upon  the  death  of 
any  one  of  the  lives  concerned. 

The  Joint  and  Survivor  Annuity,  also  called 
Annuity  on  the  Last  Survivor,  is  to  be  paid  so  long  as  any 
one  of  two  or  more  designated  persons  continues  to  live. 

Non-Forfeiture. 

A  Non-Forf citable  policy  is  one  which,  by  its 
terms,  provides  for  a  definite  surrender  value,  accruing 
after  a  stated  number  of  premiums  have  been  paid.  It 
has  been  the  practice  of  most  companies  from  an  early 
date  to  allow  an  equitable  paid-up  or  cash  surrender  value 

134 


after  the  expiration  of  a  reasonable  time,  but  a  policy  is 
not  strictly  non-forfeitable  unless  a  provision  for  a 
definite  and  automatic  paid-up,  cash  or  extended  insur- 
ance surrender  value  is  incorporated  in  the  contract. 

Incontestability 

The  policies  of  most  companies  provide  that,  dur- 
ing a  stated  number  of  years  from  date  of  issue,  the  in- 
sured shall  not  engage  in  certain  extra-hazardous  occupa- 
tions, the  policy  to  be  void  in  case  of  death  resulting  from 
a  violation  of  these  conditions,  or  in  case  of  suicide  within 
a  stated  period.  The  purpose  of  such  restrictions  is  the 
prevention  of  fraud  by  repelling  or  excluding  applicants 
who  are  seeking  insurance  for  the  very  purpose  of  de- 
frauding the  company  through  suicide,  or  for  the  very 
reason  that  they  contemplate  engaging  in  some  extra- 
hazardous occupation,  etc.  After  the  expiration  of  the 
limit  named,  such  restrictions  become  inoperative,  the 
presumption  then  being  tBat  the  policy  was  originally 
taken  out  in  good  faith.  Thereafter  the  contract  usually 
becomes  hy  its  terms  incontestable  for  any  cause,  the 
premiums  having  been  duly  paid.  The  mere  elimination 
of  restrictions,  however,  does  not  render  a  policy  incon- 
testable, an  express  provision  to  that  effect  being  neces- 
sary. Some  policies  are  wholly  free  from  restrictions 
from  date,  yet  not  incontestable  by  their  terms  until  after 
the  expiration  of  a  stated  period.  Others  are  incon- 
testable from  date  of  issue,  while  still  others  are  never 
incontestable,  even  after  stated  restrictions  have  become 
inoperative.  The  two  forms  of  contract  just  mentioned 
are  now  very  rare. 

186 


Effect  of  Fraud 

The  question  has  been  raised  as  to  whether  under 
the  rule  of  law  that  "fraud  vitiates  any  contract,"  an 
absolutely  incontestable  policy  can  be  written.  It  has 
been  held  in  Kentucky  that  a  policy,  by  its  terms  "in- 
contestable from  date,"  may  be  cancelled  for  fraud, 
while  in  Rhode  Island  a  policy,  purporting  to  be  incon- 
testable after  two  years  from  date  of  issue,  was  held  to 
be  strictly  so.  The  company  having  reserved  a  stated 
period  within  which  the  contract  should  be  contestable,  it 
would  be  presumed  that  the  period  was  a  reasonable  one 
and,  accordingly,  the  fraud  must  be  discovered  and  acted 
upon  within  that  time. 


136 


INDEX 


A 

PA«E 

Accumulated  Reserves  to  Mean  Insurance  in  Force, 

Ratio  of 65 

Actual  Cost,  -  Life  Insurance  at 113 

Actual  Mortality 68 

Actual  Saving  in  Mortality 97 

Actual  to  Expected  Mortality,  Ratio  of 71 

Adequacy  of  Net  Premium,  Proving  the 40 

Admitted  Assets 88 

Adverse  Selection 101 

Age,  the  Average 71 

American  Experience  Table  of  Mortality 11,  13 

Amount  at  Risk 66 

Annual  Dividend 107 

Annual  Statement 94 

Annuitant 20 

Annuities 130 

Annuity 30 

Annuity,  Certain 131 

Annuity,  Computation  of  Temporary 31 

Annuity,  Computing  the  Value  of 21 

Annuity,  Contingent 134 

Annuity,   Joint 134 

Annuity,  Joint  and  Survivor 134 

Annuity,  Life 30 

Annuity  on  the  Last  Survivor 134 

Annuity,  Perpetual 131 

Annuity,  Survivorship 181 

Annuity,  The  Deferred 131 


Annuity,  Temporary 29,  30 

Annuity,  Value  of 21,  24 

Assessment  Insurance 28,  54,  74,  75,  76,  77,  94,  100, 133 

Assessment  Plan 28 

Assets,  Admitted 88 

Assets  to  Liabilities,  Ratio  of 89 

Average  After  Lifetime 73 

Average  Age 71 

Average  Future  Lifetime  73 

B 

Beneficiary 6 

Booth,  Charles  H 57 

Brokerage i 118 

C 

Cash  Surrender  Value 66,  79 

Cash  Value 79 

Cash  Values  and  Endowments 56 

Certificate  of  Stock 7 

Charles  H.  Booth  Policy 57 

Claim 67 

Commission 118 

Commission,  Renewal 118 

Commuted  Values  131 

Company,  A  Hypothetical 12 

Company,  Legal  Reserve 89 

Company,  Mixed 7 

Company,  Mutual 6 

Company,  Old  Line 94 

Company,  Stock 6 

Composition  of  the  Premium 54 

Computation  of  Temporary  Annuity 31 

Computation  of  the  Premium 13 

Computing  Limited  Payment  Premiiun 81 

Computing  the  Value  of  the  Annuity 21 

ii 


PAOB 

Contingency,  Life 133 

Contingency  Reserve 88 

Contingent  Annuities 134 

Continuous  Instalment  Policy 132 

Contribution  Plan 110 

Co-Operative  Company 94 

Cost  of  Insurance 67 

Cost  of  New  Business 118 

D 

Death  Claim 67 

Death  Claims  Incurred  to  Mean  Amount  of  Insurance 

in  Force,  The  Ratio  of 68 

Deferred  Annuity 131 

Deferred  Distribution 107 

Deferred  Dividend 107 

Determining  Premium  of  Term  Policy 33 

Determining  the  Limited  Payment  Premium 31 

Determining  the  Net  Value 84 

Different  Kinds  of  PoUcies 30 

Distribution,  Deferred 107 

Distribution,  Methods  of 106 

Distribution,  Mutual  Life  Method 109 

Distribution,  Semi-Tontine 107 

Distribution,  The  Contribution  Plan 110 

Distribution,  The  Percentage  Method 110 

Distribution,   Tontine 108 

Dividend 107 

Dividend,  Annual 107 

Dividend,  Deferred 107 

Dividend,  Yearly 107 

Dying,  Probability  of 73 


Effect  of  Fraud 136 

Effect  of  Mortality  in  Endowment  Insurance 38 

Effect  of  New  Members 38 

iii 


PAGE 

Effect  of  Withdrawals 26 

Election 6 

Elementary  Principles 8 

Endowment,  Fifteen- Year 37 

Endowment  Ingurance 36 

Endowment  Insurance,  Effect  of  Mortality  in 38 

Endowment  Policies 36 

Endowment  Premium 37 

Endowment,  Pure  ...   37 

Endowments,  Cash  Values  and 56 

Endowment,  Thirty- Year 37 

Indowment,  Twenty- Year 37 

Errors,  Some  Popular 53 

Examples  of  Remarkable  Longevity 49 

Expectation  of  Life 72 

Expectation  of  Life  Not  Used  in  Computing  Cost  of 

Life  Insurance 75 

Expected  Mortality 68 

Expense  Element 53 

Expenses  Incurred  to  Loading  Earned,  Ratio  of 80 

Expiry,  Termination  by 33,  103 

r 

Face 67 

Fifteen-Year  Endowment 37 

First  Step 14 

First  Year  Term 120 

Fraternal  Insurance 94,  118 

Fraud,  Effect  of 136 

Full  Preliminary  Term 124 

Fund,  Mortality 43 

Fund,  Reserve 43 

G 

Gain,  Sources  of 96 

Gains  or  Savings  in  Life  Insurance 95 

General  Observations 24 

Gross  Premium 10 

iv 


PAGE 

H 


Hypothetical  Company 13 


Incontestability 1 35 

Initial  Reserve 44 

Insurable  Interest 129 

Insurance,  Assessment 28,  54,  74,  75,  76,  77,  94,  100,  133 

Insurance,  Cost  of 67 

Insurance,  Effect  of  Mortality  in  Endowment 38 

Insurance,  Endowment 36 

Insurance,  Natural  Premium 116 

Insurance,  Non-Participating 110 

Insurance,  Participating Ill 

Insurance,  Renewable  Term 33 

Insurance,  Stock  Rate Ill 

Insurance,  Ten- Year  Renewable  Term 33 

Insurance,  Term 32 

Insurance,  Yearly  Renewable  Term 33 

Interest  Rate 16 

Interest,  The  Insurable 129 

Introduction 3 

"  Investment  Element  " 54 


Joint  and  Survivor  Annuity 134 

Joint  Annuity 134 


Lapse 26 

Lapses  and  Terminations  by  Expiry 102 

Lapses  Not  Desirable  Source  of  Profit 100 

Legal  Net  Value 83 

Legal  Reserve 83 


PAGB 

liegal  Reserve  Company 94 

Legal  Reserve  Liability 86 

Legal  Standard  of  Valuation 83 

Level  Premium 117 

Level  Net  Premium 123 

Liability,  The  Legal  Reserve 86 

Life  Annuity 20 

Life  Contingency 133 

Life,  Expectation  of 72 

Life  Insurance  at  Actual  Cost  113 

Life  Insurance,  Origin  of 6 

Life  Insurance  Policy 6 

Life  Insurance,  Profits  in 34 

Life,  Limit  of 11,  48 

Life,  Probable 73 

Life,  Ten-Payment 30 

Life,  Twenty -Payment 80 

Limit  of  Life 11,  48 

Limited  Payment  Life  Policy 30 

Limited  Payment  Premium,  Determining  the 31 

Living,  Probability  of. 73 

Loading 9,  10,  76 

Loading,  To  Ascertain  the 78 

Loading,  True  Office  of 77 

Longevity,  Examples  of  Remarkable 49 

Loss 66,  67 

M 

Making  the  Premium 8 

Meaning  of  Large  Reserves 64 

Mean  Reserve 63 

Methods  of  Distribution 106 

Minimum  Legal  Standard 83 

Minimum  Legal  Standard  of  Valuation 81 

Mixed  Company 7 

Mixed  Table 126 

vi 


PAGE 

Modified  Preliminary  Term 124 

Mortality 68 

Mortality,  Actual 68 

Mortality,  American  Experience  Table  of 11,  13 

Mortality  Element 53 

Mortality,  Expected 68 

Mortality  Fund 43 

Mortality  in  Endo"vrment  Insurance,  Effect  of 38 

Mortality,  Saving  in 68,  96 

Mortality  at  Older  Ages,  Saving  in 103 

Mortality  Saving,  When  Greatest 99 

MortaHty  Table 10 

Mortality  Table,  American  Experience 11,  13 

Mortality  Table,  The  Mixed , 126 

Mortality  Table,  The   Select 126 

MortaUty  Table,  The   Ultimate 126 

Mortality,  Tabular 68 

Mortality,  The  Actual  Saving  in 97 

Mutual  Companies 6 

Mutual  Life  Insurance  Company 6 

Mutual  Life  Method  of  Distribution 109 

Mutual  Life  of  New  York 7 

N 

Natural  Premium 117 

Natural  Premium  Insurance 116 

Net  Annual  Premium,  to  Find  the 23 

Net  Premium 9,  10 

Net  Premium,  The  Exact 42 

Net  Premium,  Proving  the  Adequacy  of  the 40 

Net  Single  Premium 19,  59 

Net  Valuation 81 

Net  Value 81 

Net  Value,  Determining  the 84 

Net  Value,  Legal 83 

"New  Blood" 29,  52 

'•  New  Blood"  Not  Essential  to  Permanence 52 

vii 


PAGE 

New  Members,  Effect  of 28 

New  Business,  The  Cost  of 118 

Non-Forfeiture 134 

Non-Participating  Insurance 110 

O 

Observations  on  the  Reserve 52 

"  Old  Line "  Company 94 

Oldest  Policyholder 51 

One- Year  Term  Pohcy 32 

Ordinary  Life  Pohcy 8 

Origin  of  Life  Insurance 5 

Over-charge,  What  Becomes  of  the 113 


P 

Participating  Insurance Ill 

Percentage  Method 110 

Perpetual  Annuity 131 

Policies,  Different  Kinds  of 30 

Policies,  Standard 130 

Policy,  Continuous  Instalment 132 

Policy,  Determining  Premium  of  Term 33 

Policy,  Endowment 36 

Policyholder 6 

Policyholder,  The  Oldest 51 

PoUcy,  Life  Insurance 6 

Policy,  Limited  Payment  Life 30 

Pohcy,  One- Year  Term 32 

Policy,  Ordinary  Life 8 

Policy,  Ten- Year  Term 32 

Policy,  Term 32 

Policy,  The  Standard 130 

Pohcy,  Thirty- Year  Term 32 

Pohcy,  Twenty-Year  Term 32 

Preliminary  Term  System 119 

▼Hi 


PAQZ 

Preliminary  Term,  The  Full 124 

Preliminary  Term,  The  Modified 124 

Premium 6 

Premium,  Composition  of  the 54 

Premium,  Computation  of 12 

Premium,  Determining  Limited  Payment 31 

Premium,  Endowment 37 

Premium,  Gross ...     10 

Premium,  Making  the 8 

Premium,  Net 9 

Premium,  Net  Single 19 

Premium  Not  Composed  of  Three  Elements 55 

Premium,  Proving  Adequacy  of  the  Net 40 

Premium,  Stipulated 94 

Premium,  Suflaciency  of 25 

Premium.  The  Exact  Net 42 

Premium,  The  Level 117 

Premium,  The  Natural 117 

Premium,  The  Level  Net 122 

Premium,  To  Find  the  Net  Annual 23 

Probability  of  Dying 72 

Probabihty  of  Living 72 

Probable  Life 73 

Profit,  Lapses  Not  Desirable  Source  of 100 

Profits  in  Life  Insurance 34 

Profits,  To  Whom  Go 36 

Proving  the  Adequacy  of  Net  Premium 40 

Pure  Endowment 37 

R 

Rapid  Accumulation  of  Reserves 63 

Ratio,  A  Misleading 80,  99 

Ratio  of  Accumulated  Reserves  to  Mean  Insurance  in 

Force 65 

Ratio  of  Assets  to  Liabihties 89 

Ratio  of  Death  Claims  Incurred  to  Mean  Amount  of 

Insurance  in  Force 68 

ix 


PAGE 

Ratio  of  Expenses  Incurred  to  Loading  Earned 80 

Remarkable  Longevity,  Examples  of 49 

Renewable  Term  Insurance 33 

Renewal  Commission 118 

Reserve 43 

Reserve  Account 55 

Reserve  All  for  Mortality  Purposes 52 

Reserve  Basis,  How  Savings  Vary  According  to 103 

Reserve  Basis  Must  Be  Considered 90 

Reserve  Element 53 

Reserve,  Initial 44 

Reserve,  Legal 83 

Reserve,  Mean 63 

Reserve  Not  the  Property  of  Individual  Policyholder.  61 

Reserve,  Observations  on  the 52 

Reserves,  Rapid  Accumulation  of 63 

Reserves,  Single  Premiums  and 58 

Reserves,  The  Meaning  of  Large 64 

Reserve  Tables 62 

Reserve,  Terminal 44 

Reserve,  The  Contingency 88 

Reserve  Values  on  Paid-up  Policies 59 

Risk,  Amount  at 66 

S 

Saving  in  Mortality 68,  96 

Saving  in  Mortality  at  Older  Ages 102 

Saving  in  Mortality,  When  Greatest 99 

Savings  Vary  According  to  Reserve  Basis 103 

Select  and  Ultimate  Valuation 125 

Selection  Against  the  Company 101 

Select  Lives 126 

Select  Table 126 

Self  Insurance 66 

Semi-Tontine  Distribution 107 

Semi-Tontine  Plan 107 

Single  Premiums  and  Reserves 58 

X 


PAGB 

Slight  Gains  from  Saving  in  Mortality  at  the  Older  Ages  102 

So-called  "  Profits  "  in  Life  Insurance 34 

Some  Popular  Errors 53 

Sources  of  Gain 96 

Standard  Policies 130 

Statement,  The  Annual 94 

Step-Rate  Plan 118 

Stipulated  Premium 94 

Stock,  Certificate  of 7 

Stock  Companies 5^ 

Stockholder 7 

Stock  Rate  Insurance Ill 

Sufficiency  of  the  Premium 25 

Sundry  Topics 129 

Surrender  Charge 79,  101 

Surrender  Value,  Cash 56,  79 

Surplus 107 

Survivorship  Annuity 131 

Survivor,  Annuity  on  the  Last 134 

T 

Table,  Verification 41,  45,  46,  47 

Tabular  Mortality 68 

Tabulated  Illustration 91 

Temporary  Annuity 31 

Temporary  Annuity,  Computation  of 31 

Ten-Payment  Life 30 

Ten-Year  Renewable  Term 83 

Ten-Year  Term  Policy 32 

Term,  First  Year 120 

Terminal  Reserve 44 

Termination  by  Expiry 33,  102 

Term  Insurance 32 

Term  Insurance,  Renewable 33 

Term  Insurance,   Ten- Year  Renewable 33 

Term  Insurance,  Yearly  Renewable 33 

Term  Plan,  Full  Preliminary 124 

xi 


PAOB 

Term  Plan,  Modified  Preliminary 124 

Term  Policy r. 33 

Term  Policy,  Determining  Premium  of 33 

Term,  The  Preliminary 119 

The  Exact  Net  Premium 42 

Thirty-Year  Endowment 37 

Thirty-Tear  Term  Pohcy 32 

To  Ascertain  the  Loading 78 

To  Find  the  Net  Annual  Premium 23 

Tontine  Distribution 107 

Tontine  Method 108 

Topics,  Sundry 129 

Total  Insurance  Fund  18 

To  Whom  the  Profits  Go 36 

Twenty-Payment  Life 30 

Twenty- Year  Endowment 37 

Twenty-Year  Term  Policy 32 

U 

Ultimate  Table 126 

V 

Valuation,  Legal  Standard  of 83 

Valuation,  Minimum  Legal  Standard  of 81 

Valuation,  Net 81 

Valuation,  Level  Net  Premium 122 

Valuation,  Select  and  Ultimate 125 

Value  of  An  Annuity 21,  24 

Value,  The  Commuted 131 

Value,  The  Net 81 

Verification  Table.... 41,  45,  46,  47 

Vie  Probable 73 

W 

What  Becomes  of  the  Over-charge  ? 118 

When  Mortality  Saving  is  Greatest 99 

Withdrawals,  Effect  of 26 

Y 

Yearly  Dividend 107 

Yearly  Renewable  Term  Insurance 38 

zii 
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